### This work done by Omar A. AbuGhneim from Jordan University (Email: o_abughneim@yahoo.com).
    
    
# There are 267 groups of order 64. Among them, there are 259 groups that 
# admit (64,28,12) difference sets. The other 8 groups do not have any 
# (64,28,12) difference sets. We wrote programs using the software GAP 
# to construct all (64,28,12) difference sets in the 259 groups of order 
# 64 that admit (64,28,12) difference sets.
    
    
    
# We refer to the groups as they appear in the SmallGroups library of 
# the software package GAP. For instance, when we work in groups of 
# order 64 and write [64,14] we mean group number 14 of order 64 in the 
# GAP library. 
# The 8 groups that do not admit (64,28,12) difference sets are 
# [64, 1], [64, 38], [64, 47], [64, 50], [64, 52], [64, 53], [64, 54], 
# and [64, 186]. Indeed, these groups are the ones that have either 
# the cyclic group of order 32 as a factor group or have the dihedral 
# group of order 32 as a factor group. 
    
    
# Also, we find all  (64,28,12)  difference sets that are reversible 
# i.e. all  (64,28,12) difference sets D with D=D^(-1). There are 184 
# groups of order 64 that have reversible (64,28,12) difference sets. 
# These groups are [64,i] where i in {2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 
# 15, 16, 18, 20, 22, 23, 24, 25, 28, 30, 31, 32, 33, 34, 35, 36, 37, 40, 
# 41, 42, 43, 45, 46, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 
# 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 87, 
# 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, 
# 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 126, 
# 127, 128, 129, 130, 131, 133, 134, 135, 138, 140, 141, 142, 144, 145, 146, 
# 147, 149, 150, 151, 152, 153, 155, 156, 157, 159, 160, 161, 162, 163, 164, 
# 166, 167, 169, 170, 172, 173, 174, 177, 178, 179, 182, 184, 187, 190, 192, 
# 193, 194, 195, 196, 197, 199, 200, 202, 203, 204, 205, 206, 207, 208, 209, 
# 210, 211, 213, 214, 215, 216, 219, 221, 222, 226, 227, 231, 232, 234, 236, 
# 240, 241, 242, 245, 247, 249, 250, 251, 254, 260, 261, 263, 267  }. 
    
    
# We used the software GAP to find all (64,28,12)  difference sets and 
# reversible (64,28,12) difference sets.   
    
    
# In this file we list all inequivalent (64,28,12) difference sets 
# in group [64,100]. Also, we determine the nonisomorphic 
# symmetric (64,28,12) designs that rise from these DSs.
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,100].
    
    
# To determine the nonisomorphic symmetric (64,28,12) designs, we used 
# the DESIGN package for GAP, Version 1.6, 2011, by L.H. Soicher, 
# http://designtheory.org/software/gap design/. 
    
    
# Note: The GAP command 'e:=Elements(SmallGroup(64,100));' can be 
# used to create a list e of the elements of the group [64,100].
# In our list of (64,28,12) DSs in group [64,100], we have [1, 
# 2, 3, 4, 5, 6, 9, 12, 13, 14, 15, 20, 27, 29, 30, 
# 36, 39, 40, 41, 43, 50, 52, 53, 54, 55, 58, 59, 64].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[6], e[9], e[12], e[13], e[14], e[15], e[20], e[27], e[29], e[30], e[36], 
# e[39], e[40], e[41], e[43], e[50], e[52], e[53], e[54], e[55], e[58], e[59], e[64]]
# where e is the list of the elements of the group [64,100] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,100));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 100]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,100] is 1942
### The list of all inequivalent (64,28,12) DSs in group [64,100] is 
  
  
DS100:=[ [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 15, 20, 27, 29, 30, 36, 39, 40, 41, 43, 50, 52, 53, 54, 55, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 15, 20, 27, 29, 30, 33, 36, 39, 40, 41, 43, 50, 52, 55, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 15, 20, 29, 31, 36, 39, 40, 41, 43, 49, 53, 54, 55, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 15, 20, 29, 31, 33, 36, 39, 40, 41, 43, 49, 55, 58, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 18, 20, 21, 23, 24, 26, 29, 36, 37, 38, 42, 45, 47, 51, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 17, 18, 21, 24, 25, 26, 29, 36, 37, 38, 40, 47, 48, 51, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 17, 18, 20, 23, 26, 32, 36, 37, 38, 39, 43, 45, 46, 53, 54, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 17, 18, 20, 23, 24, 26, 32, 36, 37, 38, 39, 45, 47, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 20, 23, 26, 32, 36, 39, 40, 41, 43, 45, 46, 53, 54, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 20, 23, 24, 26, 32, 36, 39, 40, 41, 45, 47, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 20, 23, 26, 32, 36, 41, 43, 45, 46, 53, 54, 55, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 20, 23, 24, 26, 32, 36, 41, 45, 47, 53, 54, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 18, 23, 26, 32, 36, 42, 43, 45, 46, 53, 54, 55, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 18, 23, 24, 26, 32, 36, 42, 45, 47, 53, 54, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 18, 20, 21, 24, 26, 29, 30, 31, 32, 34, 42, 43, 44, 45, 47, 49, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 19, 20, 27, 32, 34, 37, 39, 44, 45, 48, 49, 50, 51, 54, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 19, 20, 27, 32, 33, 34, 37, 39, 44, 45, 48, 49, 50, 51, 53, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 19, 20, 25, 26, 32, 34, 37, 39, 43, 46, 47, 48, 51, 54, 57, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 19, 20, 24, 32, 34, 37, 39, 44, 45, 46, 47, 48, 51, 54, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 19, 20, 24, 25, 26, 32, 34, 37, 39, 43, 48, 51, 54, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 19, 20, 23, 27, 32, 34, 37, 39, 48, 49, 50, 51, 54, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 19, 20, 23, 24, 32, 34, 37, 39, 46, 47, 48, 51, 54, 57, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 19, 20, 27, 32, 33, 35, 36, 39, 44, 45, 48, 49, 50, 51, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 19, 20, 23, 27, 32, 33, 35, 36, 39, 48, 49, 50, 51, 54, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 18, 21, 23, 26, 32, 36, 39, 43, 45, 51, 53, 54, 55, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 18, 21, 23, 24, 26, 32, 36, 39, 45, 46, 47, 51, 53, 54, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 18, 20, 21, 23, 26, 32, 36, 42, 43, 45, 46, 51, 53, 54, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 18, 20, 21, 23, 24, 26, 32, 36, 42, 45, 47, 51, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 17, 19, 20, 27, 32, 35, 36, 40, 44, 45, 48, 49, 50, 51, 53, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 17, 19, 20, 23, 27, 32, 35, 36, 40, 48, 49, 50, 51, 53, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 17, 18, 21, 26, 32, 36, 40, 43, 44, 51, 53, 54, 55, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 17, 18, 21, 24, 25, 26, 32, 36, 40, 47, 48, 51, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 20, 24, 26, 28, 29, 30, 34, 35, 37, 39, 40, 41, 47, 51, 52, 53, 54, 56 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 17, 19, 20, 23, 24, 28, 29, 30, 37, 40, 43, 48, 51, 52, 56, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 16, 17, 20, 23, 24, 27, 29, 30, 38, 41, 43, 46, 48, 50, 52, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 16, 17, 19, 20, 23, 24, 28, 30, 38, 40, 43, 48, 50, 52, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 16, 17, 19, 20, 23, 24, 27, 30, 38, 40, 43, 46, 48, 51, 52, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 20, 24, 26, 29, 33, 35, 38, 39, 40, 41, 44, 46, 47, 53, 55, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 16, 17, 20, 23, 24, 28, 29, 30, 37, 41, 43, 46, 48, 51, 52, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 20, 26, 29, 33, 34, 35, 36, 39, 40, 41, 43, 44, 58, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 20, 24, 26, 29, 33, 34, 35, 36, 39, 40, 41, 44, 46, 47, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 20, 24, 26, 28, 29, 30, 33, 34, 35, 36, 39, 40, 41, 47, 51, 52, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 20, 23, 24, 26, 27, 30, 36, 39, 40, 41, 44, 45, 47, 51, 52, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 18, 19, 23, 24, 27, 29, 30, 41, 42, 43, 44, 48, 50, 52, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 18, 19, 20, 23, 27, 29, 30, 36, 41, 46, 47, 48, 50, 52, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 18, 19, 20, 23, 24, 27, 29, 30, 36, 41, 43, 48, 50, 52, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 17, 20, 24, 26, 28, 29, 30, 34, 35, 36, 41, 47, 51, 52, 53, 54, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 17, 20, 23, 24, 26, 27, 30, 36, 41, 44, 45, 47, 51, 52, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 17, 19, 20, 23, 24, 30, 36, 40, 44, 45, 48, 49, 50, 51, 52, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 17, 19, 20, 23, 24, 28, 29, 30, 36, 40, 43, 48, 51, 52, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 17, 19, 20, 23, 24, 27, 30, 36, 40, 44, 45, 48, 51, 52, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 16, 18, 24, 29, 37, 38, 39, 40, 42, 45, 48, 53, 59, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 16, 18, 23, 24, 29, 37, 38, 39, 40, 42, 43, 44, 48, 53, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 16, 17, 18, 23, 24, 29, 37, 38, 42, 43, 44, 48, 53, 57, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 20, 25, 26, 29, 33, 34, 36, 37, 38, 39, 40, 41, 43, 46, 48, 53, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 20, 24, 26, 28, 29, 30, 33, 34, 36, 37, 38, 39, 40, 41, 47, 51, 52, 53 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 20, 24, 25, 26, 29, 33, 34, 36, 37, 38, 39, 40, 41, 47, 48, 53, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 18, 25, 26, 29, 33, 34, 36, 37, 38, 39, 40, 42, 43, 46, 48, 53, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 18, 21, 24, 27, 29, 31, 34, 35, 36, 37, 38, 39, 48, 49, 52, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 18, 20, 21, 23, 24, 25, 27, 30, 38, 42, 43, 45, 46, 51, 52, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 20, 25, 26, 29, 34, 36, 37, 38, 41, 43, 46, 48, 54, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 20, 24, 26, 28, 29, 30, 33, 34, 36, 37, 38, 41, 47, 51, 52, 53, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 19, 20, 24, 28, 29, 30, 34, 36, 37, 38, 40, 48, 51, 52, 54, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 19, 20, 24, 28, 29, 30, 33, 34, 36, 37, 38, 40, 48, 51, 52, 53, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 19, 20, 24, 25, 26, 28, 30, 38, 40, 43, 48, 50, 52, 55, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 19, 20, 24, 25, 26, 27, 30, 38, 40, 43, 46, 48, 51, 52, 55, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 19, 20, 23, 28, 30, 38, 40, 43, 48, 50, 52, 55, 58, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 19, 20, 23, 24, 28, 30, 38, 40, 46, 47, 48, 50, 52, 55, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 18, 20, 24, 26, 29, 36, 37, 38, 39, 44, 46, 47, 53, 54, 55, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 18, 20, 24, 25, 26, 29, 36, 37, 38, 39, 47, 48, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 15, 20, 24, 26, 28, 29, 30, 33, 37, 39, 40, 41, 47, 51, 52, 55, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 15, 20, 24, 26, 27, 29, 34, 39, 40, 41, 44, 49, 50, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 15, 20, 24, 26, 27, 29, 34, 39, 40, 41, 43, 44, 49, 50, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 15, 20, 24, 25, 26, 27, 29, 30, 34, 39, 40, 41, 43, 48, 50, 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54, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 27, 36, 37, 38, 41, 43, 46, 50, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 30, 34, 37, 38, 40, 43, 46, 52, 55, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 28, 36, 37, 38, 40, 43, 46, 51, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 28, 35, 37, 38, 39, 42, 43, 48, 49, 51, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 28, 33, 35, 37, 38, 39, 42, 48, 49, 51, 53, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 37, 40, 41, 46, 49, 52, 55, 56, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 37, 40, 41, 43, 49, 52, 55, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 37, 40, 41, 43, 46, 52, 55, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 36, 37, 40, 41, 46, 49, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 36, 37, 40, 41, 43, 49, 52, 53, 55, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 33, 34, 36, 40, 41, 47, 49, 52, 55, 56, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 24, 30, 33, 34, 36, 40, 41, 49, 52, 55, 56, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 35, 37, 38, 39, 41, 43, 48, 49, 52, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 33, 35, 37, 38, 39, 41, 48, 49, 52, 53, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 27, 35, 36, 38, 39, 41, 47, 48, 49, 50, 53, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 30, 34, 37, 40, 46, 49, 52, 53, 55, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 28, 35, 36, 38, 39, 40, 47, 48, 49, 51, 53, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 20, 21, 28, 35, 36, 43, 44, 51, 55, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 19, 30, 34, 36, 37, 41, 43, 49, 52, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 19, 30, 33, 38, 40, 41, 47, 49, 52, 53, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 19, 24, 30, 33, 38, 40, 41, 49, 52, 53, 60, 63, 64 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1265
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS100[1], DS100[5], DS100[6], DS100[19], DS100[20], DS100[24], DS100[25], DS100[26], DS100[27], DS100[31], DS100[32], DS100[34], DS100[36], DS100[37], DS100[43], DS100[44], DS100[48], DS100[51], DS100[52], DS100[59], DS100[60], DS100[63], DS100[64], DS100[72], DS100[73], DS100[74], DS100[75], DS100[76], DS100[83], DS100[85], DS100[87], DS100[89], DS100[90], DS100[92], DS100[98], DS100[99], DS100[102], DS100[103], DS100[105], DS100[106], DS100[110], DS100[111], DS100[112], DS100[124], DS100[130], DS100[136], DS100[137], DS100[138], DS100[142], DS100[143], DS100[150], DS100[151], DS100[152], DS100[154], DS100[155], DS100[156], DS100[157], DS100[158], DS100[160], DS100[161], DS100[164], DS100[165], DS100[166], DS100[168], DS100[169], DS100[176], DS100[178], DS100[179], DS100[180], DS100[181], DS100[182], DS100[183], DS100[186], DS100[188], DS100[191], DS100[196], DS100[197], DS100[198], DS100[199], DS100[205], DS100[206], DS100[208], DS100[223], DS100[224], DS100[225], DS100[226], DS100[227], DS100[235], DS100[236], DS100[237], DS100[238], DS100[240], DS100[242], DS100[243], DS100[244], DS100[246], DS100[249], DS100[250], DS100[258], DS100[259], DS100[260], DS100[261], DS100[264], DS100[265], DS100[266], DS100[267], DS100[268], DS100[269], DS100[270], DS100[271], DS100[272], DS100[273], DS100[274], DS100[278], DS100[281], DS100[282], DS100[284], DS100[289], DS100[291], DS100[293], DS100[297], DS100[298], DS100[299], DS100[300], DS100[301], DS100[311], DS100[312], DS100[313], DS100[314], DS100[315], DS100[316], DS100[317], DS100[318], DS100[319], DS100[320], DS100[321], DS100[322], DS100[323], DS100[324], DS100[325], DS100[326], DS100[327], DS100[328], DS100[329], DS100[330], DS100[331], DS100[332], DS100[333], DS100[334], DS100[335], DS100[336], DS100[337], DS100[338], DS100[339], DS100[340], DS100[345], DS100[346], DS100[349], DS100[352], DS100[354], DS100[357], DS100[358], DS100[362], DS100[363], DS100[364], DS100[367], DS100[371], DS100[377], DS100[378], DS100[383], DS100[384], DS100[386], DS100[387], DS100[392], DS100[393], DS100[395], DS100[397], DS100[398], DS100[405], DS100[406], DS100[409], DS100[410], DS100[411], DS100[412], DS100[413], DS100[419], DS100[421], DS100[422], DS100[426], DS100[427], DS100[429], DS100[430], DS100[431], DS100[433], DS100[434], DS100[435], DS100[436], DS100[437], DS100[438], DS100[439], DS100[440], DS100[441], DS100[442], DS100[443], DS100[445], DS100[446], DS100[447], DS100[448], DS100[450], DS100[452], DS100[454], DS100[455], DS100[456], DS100[457], DS100[458], DS100[459], DS100[460], DS100[461], DS100[462], DS100[463], DS100[464], DS100[465], DS100[466], DS100[467], DS100[473], DS100[474], DS100[476], DS100[478], DS100[480], DS100[481], DS100[482], DS100[483], DS100[487], DS100[492], DS100[493], DS100[494], DS100[495], DS100[496], DS100[497], DS100[503], DS100[505], DS100[508], DS100[511], DS100[512], DS100[514], DS100[515], DS100[516], DS100[517], DS100[519], DS100[524], DS100[526], DS100[528], DS100[529], DS100[530], DS100[531], DS100[533], DS100[534], DS100[535], DS100[536], DS100[537], DS100[538], DS100[539], DS100[540], DS100[541], DS100[542], DS100[544], DS100[548], DS100[550], DS100[553], DS100[555], DS100[556], DS100[557], DS100[559], DS100[560], DS100[561], DS100[562], DS100[563], DS100[564], DS100[566], DS100[567], DS100[568], DS100[569], DS100[570], DS100[571], DS100[572], DS100[573], DS100[574], DS100[575], DS100[576], DS100[577], DS100[582], DS100[584], DS100[587], DS100[588], DS100[590], DS100[591], DS100[592], DS100[594], DS100[595], DS100[597], DS100[598], DS100[603], DS100[606], DS100[607], DS100[609], DS100[610], DS100[612], DS100[613], DS100[615], DS100[616], DS100[617], DS100[618], DS100[619], DS100[620], DS100[621], DS100[622], DS100[623], DS100[624], DS100[625], DS100[626], DS100[627], DS100[628], DS100[630], DS100[631], DS100[632], DS100[633], DS100[635], DS100[636], DS100[638], DS100[639], DS100[641], DS100[642], DS100[643], DS100[644], DS100[645], DS100[646], DS100[647], DS100[648], DS100[649], DS100[650], DS100[651], DS100[655], DS100[656], DS100[657], DS100[658], DS100[659], DS100[661], DS100[662], DS100[663], DS100[664], DS100[665], DS100[669], DS100[670], DS100[671], DS100[672], DS100[673], DS100[674], DS100[678], DS100[680], DS100[683], DS100[684], DS100[686], DS100[687], DS100[692], DS100[695], DS100[703], DS100[704], DS100[705], DS100[707], DS100[710], DS100[711], DS100[712], DS100[714], DS100[715], DS100[716], DS100[717], DS100[718], DS100[719], DS100[720], DS100[721], DS100[723], DS100[724], DS100[728], DS100[729], DS100[731], DS100[732], DS100[733], DS100[735], DS100[736], DS100[737], DS100[738], DS100[739], DS100[740], DS100[741], DS100[742], DS100[743], DS100[744], DS100[752], DS100[753], DS100[755], DS100[756], DS100[757], DS100[758], DS100[759], DS100[762], DS100[764], DS100[766], DS100[767], DS100[770], DS100[771], DS100[772], DS100[773], DS100[774], DS100[775], DS100[776], DS100[777], DS100[778], DS100[779], DS100[780], DS100[781], DS100[782], DS100[783], DS100[785], DS100[787], DS100[788], DS100[789], DS100[790], DS100[791], DS100[792], DS100[793], DS100[794], DS100[795], DS100[796], DS100[797], DS100[798], DS100[799], DS100[800], DS100[804], DS100[805], DS100[808], DS100[811], DS100[812], DS100[816], DS100[818], DS100[824], DS100[828], DS100[829], DS100[832], DS100[838], DS100[847], DS100[849], DS100[850], DS100[855], DS100[856], DS100[857], DS100[858], DS100[859], DS100[862], DS100[863], DS100[864], DS100[865], DS100[866], DS100[867], DS100[868], DS100[869], DS100[870], DS100[871], DS100[872], DS100[873], DS100[874], DS100[875], DS100[878], DS100[881], DS100[884], DS100[886], DS100[888], DS100[889], DS100[890], DS100[891], DS100[892], DS100[894], DS100[896], DS100[897], DS100[904], DS100[905], DS100[906], DS100[907], DS100[908], DS100[909], DS100[910], DS100[911], DS100[912], DS100[913], DS100[914], DS100[915], DS100[916], DS100[917], DS100[918], DS100[919], DS100[920], DS100[921], DS100[922], DS100[923], DS100[924], DS100[925], DS100[926], DS100[931], DS100[932], DS100[933], DS100[935], DS100[937], DS100[942], DS100[943], DS100[944], DS100[945], DS100[949], DS100[950], DS100[957], DS100[958], DS100[965], DS100[966], DS100[968], DS100[969], DS100[970], DS100[974], DS100[977], DS100[979], DS100[984], DS100[985], DS100[986], DS100[987], DS100[988], DS100[990], DS100[991], DS100[993], DS100[994], DS100[995], DS100[996], DS100[998], DS100[999], DS100[1002], DS100[1003], DS100[1004], DS100[1005], DS100[1010], DS100[1015], DS100[1016], DS100[1017], DS100[1018], DS100[1019], DS100[1020], DS100[1021], DS100[1022], DS100[1023], DS100[1024], DS100[1025], DS100[1026], DS100[1027], DS100[1028], DS100[1029], DS100[1030], DS100[1031], DS100[1032], DS100[1033], DS100[1034], DS100[1035], DS100[1036], DS100[1037], DS100[1039], DS100[1041], DS100[1042], DS100[1043], DS100[1044], DS100[1046], DS100[1047], DS100[1048], DS100[1049], DS100[1053], DS100[1057], DS100[1062], DS100[1063], DS100[1065], DS100[1066], DS100[1069], DS100[1070], DS100[1072], DS100[1074], DS100[1077], DS100[1078], DS100[1079], DS100[1080], DS100[1081], DS100[1082], DS100[1083], DS100[1084], DS100[1085], DS100[1086], DS100[1087], DS100[1088], DS100[1089], DS100[1090], DS100[1091], DS100[1092], DS100[1093], DS100[1094], DS100[1095], DS100[1096], DS100[1097], DS100[1098], DS100[1099], DS100[1100], DS100[1101], DS100[1102], DS100[1103], DS100[1104], DS100[1105], DS100[1106], DS100[1107], DS100[1108], DS100[1109], DS100[1110], DS100[1111], DS100[1112], DS100[1113], DS100[1114], DS100[1115], DS100[1116], DS100[1117], DS100[1118], DS100[1119], DS100[1120], DS100[1121], DS100[1123], DS100[1124], DS100[1125], DS100[1126], DS100[1127], DS100[1128], DS100[1129], DS100[1130], DS100[1132], DS100[1133], DS100[1135], DS100[1136], DS100[1137], DS100[1139], DS100[1140], DS100[1142], DS100[1143], DS100[1144], DS100[1150], DS100[1151], DS100[1152], DS100[1153], DS100[1155], DS100[1156], DS100[1157], DS100[1160], DS100[1162], DS100[1164], DS100[1166], DS100[1167], DS100[1168], DS100[1169], DS100[1170], DS100[1171], DS100[1172], DS100[1173], DS100[1174], DS100[1176], DS100[1179], DS100[1181], DS100[1182], DS100[1183], DS100[1184], DS100[1185], DS100[1186], DS100[1187], DS100[1188], DS100[1189], DS100[1192], DS100[1193], DS100[1194], DS100[1195], DS100[1196], DS100[1197], DS100[1198], DS100[1199], DS100[1200], DS100[1201], DS100[1203], DS100[1206], DS100[1207], DS100[1208], DS100[1209], DS100[1210], DS100[1211], DS100[1214], DS100[1215], DS100[1216], DS100[1217], DS100[1218], DS100[1219], DS100[1220], DS100[1221], DS100[1222], DS100[1223], DS100[1224], DS100[1225], DS100[1226], DS100[1227], DS100[1228], DS100[1229], DS100[1230], DS100[1231], DS100[1232], DS100[1233], DS100[1234], DS100[1235], DS100[1236], DS100[1238], DS100[1239], DS100[1240], DS100[1241], DS100[1242], DS100[1244], DS100[1245], DS100[1246], DS100[1247], DS100[1249], DS100[1250], DS100[1251], DS100[1252], DS100[1253], DS100[1254], DS100[1255], DS100[1256], DS100[1257], DS100[1258], DS100[1259], DS100[1260], DS100[1261], DS100[1262], DS100[1263], DS100[1264], DS100[1265], DS100[1266], DS100[1267], DS100[1268], DS100[1270], DS100[1271], DS100[1273], DS100[1274], DS100[1275], DS100[1276], DS100[1277], DS100[1278], DS100[1279], DS100[1280], DS100[1281], DS100[1283], DS100[1284], DS100[1285], DS100[1286], DS100[1287], DS100[1288], DS100[1289], DS100[1290], DS100[1291], DS100[1292], DS100[1293], DS100[1294], DS100[1295], DS100[1296], DS100[1297], DS100[1298], DS100[1299], DS100[1300], DS100[1301], DS100[1302], DS100[1303], DS100[1304], DS100[1306], DS100[1307], DS100[1308], DS100[1309], DS100[1310], DS100[1311], DS100[1312], DS100[1313], DS100[1314], DS100[1315], DS100[1316], DS100[1317], DS100[1318], DS100[1319], DS100[1321], DS100[1322], DS100[1324], DS100[1325], DS100[1326], DS100[1328], DS100[1329], DS100[1330], DS100[1331], DS100[1332], DS100[1333], DS100[1334], DS100[1335], DS100[1336], DS100[1337], DS100[1338], DS100[1339], DS100[1340], DS100[1341], DS100[1342], DS100[1344], DS100[1345], DS100[1346], DS100[1347], DS100[1348], DS100[1349], DS100[1350], DS100[1351], DS100[1352], DS100[1353], DS100[1354], DS100[1355], DS100[1356], DS100[1357], DS100[1358], DS100[1359], DS100[1360], DS100[1361], DS100[1362], DS100[1363], DS100[1364], DS100[1366], DS100[1367], DS100[1368], DS100[1369], DS100[1370], DS100[1371], DS100[1372], DS100[1373], DS100[1374], DS100[1375], DS100[1376], DS100[1377], DS100[1378], DS100[1379], DS100[1380], DS100[1381], DS100[1382], DS100[1383], DS100[1384], DS100[1386], DS100[1387], DS100[1388], DS100[1389], DS100[1390], DS100[1391], DS100[1392], DS100[1394], DS100[1395], DS100[1396], DS100[1397], DS100[1398], DS100[1399], DS100[1400], DS100[1401], DS100[1402], DS100[1403], DS100[1404], DS100[1405], DS100[1406], DS100[1408], DS100[1412], DS100[1413], DS100[1415], DS100[1416], DS100[1417], DS100[1418], DS100[1419], DS100[1420], DS100[1421], DS100[1422], DS100[1423], DS100[1424], DS100[1425], DS100[1426], DS100[1427], DS100[1428], DS100[1429], DS100[1431], DS100[1432], DS100[1433], DS100[1434], DS100[1435], DS100[1436], DS100[1437], DS100[1438], DS100[1439], DS100[1440], DS100[1441], DS100[1442], DS100[1443], DS100[1444], DS100[1445], DS100[1446], DS100[1447], DS100[1448], DS100[1449], DS100[1450], DS100[1451], DS100[1452], DS100[1453], DS100[1454], DS100[1455], DS100[1456], DS100[1457], DS100[1458], DS100[1459], DS100[1460], DS100[1461], DS100[1462], DS100[1463], DS100[1464], DS100[1465], DS100[1466], DS100[1467], DS100[1468], DS100[1469], DS100[1470], DS100[1471], DS100[1472], DS100[1473], DS100[1474], DS100[1475], DS100[1476], DS100[1477], DS100[1478], DS100[1479], DS100[1480], DS100[1481], DS100[1482], DS100[1483], DS100[1484], DS100[1485], DS100[1486], DS100[1487], DS100[1488], DS100[1489], DS100[1490], DS100[1491], DS100[1492], DS100[1493], DS100[1494], DS100[1495], DS100[1497], DS100[1498], DS100[1499], DS100[1500], DS100[1503], DS100[1504], DS100[1507], DS100[1510], DS100[1523], DS100[1524], DS100[1525], DS100[1534], DS100[1535], DS100[1536], DS100[1538], DS100[1539], DS100[1541], DS100[1542], DS100[1543], DS100[1544], DS100[1545], DS100[1546], DS100[1547], DS100[1548], DS100[1549], DS100[1550], DS100[1551], DS100[1552], DS100[1553], DS100[1554], DS100[1555], DS100[1556], DS100[1557], DS100[1558], DS100[1559], DS100[1561], DS100[1562], DS100[1563], DS100[1564], DS100[1565], DS100[1566], DS100[1567], DS100[1568], DS100[1569], DS100[1570], DS100[1571], DS100[1573], DS100[1574], DS100[1575], DS100[1576], DS100[1578], DS100[1579], DS100[1580], DS100[1581], DS100[1582], DS100[1583], DS100[1584], DS100[1585], DS100[1586], DS100[1587], DS100[1588], DS100[1589], DS100[1591], DS100[1592], DS100[1593], DS100[1594], DS100[1595], DS100[1596], DS100[1597], DS100[1598], DS100[1599], DS100[1600], DS100[1601], DS100[1602], DS100[1603], DS100[1604], DS100[1605], DS100[1606], DS100[1608], DS100[1609], DS100[1610], DS100[1612], DS100[1615], DS100[1620], DS100[1621], DS100[1622], DS100[1623], DS100[1624], DS100[1628], DS100[1630], DS100[1631], DS100[1634], DS100[1636], DS100[1637], DS100[1638], DS100[1639], DS100[1641], DS100[1642], DS100[1643], DS100[1647], DS100[1648], DS100[1649], DS100[1652], DS100[1653], DS100[1656], DS100[1659], DS100[1665], DS100[1669], DS100[1670], DS100[1671], DS100[1672], DS100[1673], DS100[1676], DS100[1678], DS100[1679], DS100[1680], DS100[1681], DS100[1684], DS100[1689], DS100[1691], DS100[1692], DS100[1693], DS100[1694], DS100[1695], DS100[1696], DS100[1697], DS100[1698], DS100[1699], DS100[1700], DS100[1703], DS100[1704], DS100[1705], DS100[1706], DS100[1707], DS100[1708], DS100[1709], DS100[1710], DS100[1711], DS100[1712], DS100[1724], DS100[1728], DS100[1736], DS100[1743], DS100[1752], DS100[1753], DS100[1756], DS100[1758], DS100[1767], DS100[1770], DS100[1771], DS100[1772], DS100[1773], DS100[1774], DS100[1775], DS100[1776], DS100[1777], DS100[1778], DS100[1779], DS100[1780], DS100[1781], DS100[1782], DS100[1783], DS100[1784], DS100[1785], DS100[1786], DS100[1787], DS100[1788], DS100[1789], DS100[1790], DS100[1791], DS100[1792], DS100[1794], DS100[1795], DS100[1796], DS100[1797], DS100[1798], DS100[1799], DS100[1800], DS100[1801], DS100[1802], DS100[1803], DS100[1804], DS100[1805], DS100[1806], DS100[1807], DS100[1808], DS100[1809], DS100[1810], DS100[1811], DS100[1812], DS100[1813], DS100[1814], DS100[1815], DS100[1816], DS100[1817], DS100[1818], DS100[1819], DS100[1820], DS100[1821], DS100[1822], DS100[1823], DS100[1824], DS100[1826], DS100[1827], DS100[1828], DS100[1832], DS100[1833], DS100[1834], DS100[1835], DS100[1836], DS100[1837], DS100[1838], DS100[1839], DS100[1840], DS100[1841], DS100[1842], DS100[1843], DS100[1844], DS100[1845], DS100[1846], DS100[1847], DS100[1848], DS100[1849], DS100[1850], DS100[1851], DS100[1852], DS100[1853], DS100[1854], DS100[1855], DS100[1856], DS100[1857], DS100[1858], DS100[1859], DS100[1860], DS100[1862], DS100[1864], DS100[1865], DS100[1866], DS100[1867], DS100[1868], DS100[1869], DS100[1870], DS100[1871], DS100[1872], DS100[1873], DS100[1874], DS100[1876], DS100[1877], DS100[1878], DS100[1879], DS100[1881], DS100[1885], DS100[1886], DS100[1887], DS100[1888], DS100[1890], DS100[1891], DS100[1892], DS100[1893], DS100[1894], DS100[1895], DS100[1896], DS100[1897], DS100[1898], DS100[1899], DS100[1902], DS100[1903], DS100[1904], DS100[1905], DS100[1906], DS100[1907], DS100[1908], DS100[1909], DS100[1910], DS100[1911], DS100[1912], DS100[1913], DS100[1914], DS100[1915], DS100[1916], DS100[1917], DS100[1918], DS100[1919], DS100[1920], DS100[1921], DS100[1922], DS100[1923], DS100[1924], DS100[1925], DS100[1926], DS100[1927], DS100[1928], DS100[1929], DS100[1930], DS100[1931], DS100[1932], DS100[1933], DS100[1934], DS100[1935], DS100[1936], DS100[1937], DS100[1938], DS100[1939], DS100[1940], DS100[1941], DS100[1942]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,100].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,100] is 324
### The list of all inequivalent reversible (64,28,12) DSs in group [64,100] is 
  
  
RDS100:=[ [ 2, 3, 8, 9, 10, 11, 14, 15, 16, 17, 20, 25, 30, 33, 37, 38, 40, 42, 44, 45, 47, 49, 50, 51, 54, 58, 59, 61 ], [ 2, 3, 8, 9, 10, 11, 14, 15, 16, 17, 20, 24, 30, 33, 37, 38, 40, 42, 43, 45, 48, 49, 50, 51, 54, 58, 60, 61 ], [ 2, 3, 8, 9, 10, 11, 14, 15, 16, 17, 20, 23, 25, 30, 33, 37, 38, 40, 42, 43, 47, 49, 50, 51, 54, 60, 61, 64 ], [ 2, 3, 8, 9, 10, 11, 14, 15, 16, 17, 20, 23, 24, 30, 33, 37, 38, 40, 42, 44, 48, 49, 50, 51, 54, 59, 61, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 25, 30, 35, 37, 39, 40, 44, 45, 47, 49, 50, 51, 53, 57, 58, 59, 61, 63 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 24, 30, 35, 37, 39, 40, 43, 45, 48, 49, 50, 51, 53, 57, 58, 60, 61, 63 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 25, 30, 35, 37, 39, 40, 43, 47, 49, 50, 51, 53, 57, 60, 61, 63, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 25, 27, 30, 35, 37, 39, 40, 43, 47, 51, 53, 57, 60, 61, 62, 63, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 24, 30, 35, 37, 39, 40, 44, 48, 49, 50, 51, 53, 57, 59, 61, 63, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 23, 24, 27, 30, 35, 37, 39, 40, 44, 48, 51, 53, 57, 59, 61, 62, 63, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 20, 25, 30, 35, 36, 37, 40, 42, 44, 45, 47, 49, 50, 51, 56, 58, 59, 61 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 20, 24, 30, 35, 36, 37, 40, 42, 43, 45, 48, 49, 50, 51, 56, 58, 60, 61 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 20, 23, 25, 30, 35, 36, 37, 40, 42, 43, 47, 49, 50, 51, 56, 60, 61, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 20, 23, 25, 27, 30, 35, 36, 37, 40, 42, 43, 47, 51, 56, 60, 61, 62, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 20, 23, 24, 30, 35, 36, 37, 40, 42, 44, 48, 49, 50, 51, 56, 59, 61, 64 ], [ 2, 3, 8, 9, 10, 11, 13, 14, 16, 17, 20, 23, 24, 27, 30, 35, 36, 37, 40, 42, 44, 48, 51, 56, 59, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 20, 22, 25, 30, 33, 36, 42, 44, 45, 47, 49, 50, 51, 53, 54, 56, 58, 59, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 20, 22, 23, 25, 30, 33, 36, 42, 43, 47, 49, 50, 51, 53, 54, 56, 60, 61, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 20, 22, 23, 24, 30, 33, 36, 42, 44, 48, 49, 50, 51, 53, 54, 56, 59, 61, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 25, 30, 36, 39, 40, 42, 44, 45, 47, 49, 50, 51, 56, 57, 58, 59, 61 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 23, 25, 30, 36, 39, 40, 42, 43, 47, 49, 50, 51, 56, 57, 60, 61, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 23, 25, 27, 30, 36, 39, 40, 42, 43, 47, 51, 56, 57, 60, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 23, 24, 30, 36, 39, 40, 42, 44, 48, 49, 50, 51, 56, 57, 59, 61, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 16, 17, 20, 22, 23, 24, 27, 30, 36, 39, 40, 42, 44, 48, 51, 56, 57, 59, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 14, 16, 17, 22, 25, 30, 33, 36, 37, 40, 44, 45, 47, 49, 50, 51, 54, 56, 58, 59, 61 ], [ 2, 3, 6, 8, 9, 10, 11, 14, 16, 17, 22, 24, 30, 33, 36, 37, 40, 43, 45, 48, 49, 50, 51, 54, 56, 58, 60, 61 ], [ 2, 3, 6, 8, 9, 10, 11, 14, 16, 17, 22, 23, 25, 30, 33, 36, 37, 40, 43, 47, 49, 50, 51, 54, 56, 60, 61, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 14, 16, 17, 22, 23, 24, 30, 33, 36, 37, 40, 44, 48, 49, 50, 51, 54, 56, 59, 61, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 24, 30, 35, 38, 42, 43, 45, 48, 49, 50, 51, 53, 58, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 23, 25, 30, 35, 38, 42, 43, 47, 49, 50, 51, 53, 60, 61, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 23, 25, 27, 30, 35, 38, 42, 43, 47, 51, 53, 60, 61, 62, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 23, 24, 30, 35, 38, 42, 44, 48, 49, 50, 51, 53, 59, 61, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 15, 16, 20, 22, 23, 24, 27, 30, 35, 38, 42, 44, 48, 51, 53, 59, 61, 62, 63, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 22, 25, 30, 35, 37, 38, 40, 44, 45, 47, 49, 50, 51, 58, 59, 61 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 22, 24, 30, 35, 37, 38, 40, 43, 45, 48, 49, 50, 51, 58, 60, 61 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 22, 23, 25, 30, 35, 37, 38, 40, 43, 47, 49, 50, 51, 60, 61, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 22, 23, 25, 27, 30, 35, 37, 38, 40, 43, 47, 51, 60, 61, 62, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 22, 23, 24, 30, 35, 37, 38, 40, 44, 48, 49, 50, 51, 59, 61, 64 ], [ 2, 3, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 22, 23, 24, 27, 30, 35, 37, 38, 40, 44, 48, 51, 59, 61, 62, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 14, 15, 16, 17, 21, 25, 30, 37, 38, 40, 44, 45, 47, 49, 50, 51, 53, 58, 59, 61, 63 ], [ 2, 3, 5, 8, 9, 10, 11, 14, 15, 16, 17, 21, 24, 30, 37, 38, 40, 43, 45, 48, 49, 50, 51, 53, 58, 60, 61, 63 ], [ 2, 3, 5, 8, 9, 10, 11, 14, 15, 16, 17, 21, 23, 25, 30, 37, 38, 40, 43, 47, 49, 50, 51, 53, 60, 61, 63, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 14, 15, 16, 17, 21, 23, 24, 30, 37, 38, 40, 44, 48, 49, 50, 51, 53, 59, 61, 63, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 21, 25, 30, 35, 36, 37, 39, 44, 45, 47, 49, 50, 51, 56, 57, 58, 59, 61 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 21, 24, 30, 35, 36, 37, 39, 43, 45, 48, 49, 50, 51, 56, 57, 58, 60, 61 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 21, 23, 25, 30, 35, 36, 37, 39, 43, 47, 49, 50, 51, 56, 57, 60, 61, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 21, 23, 25, 27, 30, 35, 36, 37, 39, 43, 47, 51, 56, 57, 60, 61, 62, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 21, 23, 24, 30, 35, 36, 37, 39, 44, 48, 49, 50, 51, 56, 57, 59, 61, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 21, 23, 24, 27, 30, 35, 36, 37, 39, 44, 48, 51, 56, 57, 59, 61, 62, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 20, 21, 25, 30, 35, 37, 42, 44, 45, 47, 49, 50, 51, 53, 58, 59, 61, 63 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 20, 21, 24, 30, 35, 37, 42, 43, 45, 48, 49, 50, 51, 53, 58, 60, 61, 63 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 20, 21, 23, 25, 30, 35, 37, 42, 43, 47, 49, 50, 51, 53, 60, 61, 63, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 20, 21, 23, 25, 27, 30, 35, 37, 42, 43, 47, 51, 53, 60, 61, 62, 63, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 20, 21, 23, 24, 30, 35, 37, 42, 44, 48, 49, 50, 51, 53, 59, 61, 63, 64 ], [ 2, 3, 5, 8, 9, 10, 11, 13, 14, 16, 20, 21, 23, 24, 27, 30, 35, 37, 42, 44, 48, 51, 53, 59, 61, 62, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 16, 17, 20, 21, 22, 25, 30, 33, 40, 42, 44, 45, 47, 49, 50, 51, 54, 58, 59, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 16, 17, 20, 21, 22, 24, 30, 33, 40, 42, 43, 45, 48, 49, 50, 51, 54, 58, 60, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 16, 17, 20, 21, 22, 23, 25, 30, 33, 40, 42, 43, 47, 49, 50, 51, 54, 60, 61, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 16, 17, 20, 21, 22, 23, 24, 30, 33, 40, 42, 44, 48, 49, 50, 51, 54, 59, 61, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 16, 17, 20, 21, 22, 23, 24, 27, 30, 33, 40, 42, 44, 48, 51, 54, 59, 61, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 21, 22, 25, 30, 33, 37, 44, 45, 47, 49, 50, 51, 53, 54, 58, 59, 61, 63 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 21, 22, 23, 25, 30, 33, 37, 43, 47, 49, 50, 51, 53, 54, 60, 61, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 21, 22, 23, 24, 30, 33, 37, 44, 48, 49, 50, 51, 53, 54, 59, 61, 63, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 17, 21, 22, 25, 30, 37, 39, 40, 44, 45, 47, 49, 50, 51, 57, 58, 59, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 17, 21, 22, 23, 25, 30, 37, 39, 40, 43, 47, 49, 50, 51, 57, 60, 61, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 17, 21, 22, 23, 25, 27, 30, 37, 39, 40, 43, 47, 51, 57, 60, 61, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 17, 21, 22, 23, 24, 30, 37, 39, 40, 44, 48, 49, 50, 51, 57, 59, 61, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 16, 17, 21, 22, 23, 24, 27, 30, 37, 39, 40, 44, 48, 51, 57, 59, 61, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 21, 22, 25, 30, 34, 35, 37, 44, 45, 47, 49, 50, 51, 55, 58, 59, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 21, 22, 23, 25, 30, 34, 35, 37, 43, 47, 49, 50, 51, 55, 60, 61, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 21, 22, 23, 25, 27, 30, 34, 35, 37, 43, 47, 51, 55, 60, 61, 62, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 21, 22, 23, 24, 30, 34, 35, 37, 44, 48, 49, 50, 51, 55, 59, 61, 64 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 21, 22, 23, 24, 27, 30, 34, 35, 37, 44, 48, 51, 55, 59, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 11, 13, 16, 17, 18, 19, 20, 23, 25, 27, 31, 35, 40, 41, 42, 43, 47, 51, 52, 60, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 11, 13, 16, 17, 18, 19, 20, 23, 24, 27, 31, 35, 40, 41, 42, 44, 48, 51, 52, 59, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 10, 11, 16, 17, 19, 25, 30, 33, 36, 40, 44, 45, 47, 49, 50, 51, 53, 54, 56, 58, 59, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 11, 16, 17, 19, 24, 30, 33, 36, 40, 43, 45, 48, 49, 50, 51, 53, 54, 56, 58, 60, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 11, 16, 17, 19, 23, 25, 30, 33, 36, 40, 43, 47, 49, 50, 51, 53, 54, 56, 60, 61, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 11, 16, 17, 19, 23, 24, 30, 33, 36, 40, 44, 48, 49, 50, 51, 53, 54, 56, 59, 61, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 11, 16, 17, 19, 20, 25, 30, 33, 39, 40, 42, 44, 45, 47, 49, 50, 51, 54, 57, 58, 59, 61 ], [ 2, 3, 4, 8, 9, 10, 11, 16, 17, 19, 20, 24, 30, 33, 39, 40, 42, 43, 45, 48, 49, 50, 51, 54, 57, 58, 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