### 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 [64,11]. 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 [64,11].
    
    
# 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(64,11));' can be 
# used to create a list e of the elements of the group [64,11].
# In our list of (64,28,12) DSs in group [64,11], we have [1, 
# 2, 3, 4, 5, 7, 8, 15, 16, 19, 21, 23, 24, 25, 27, 
# 28, 29, 30, 31, 32, 38, 39, 44, 46, 57, 59, 62, 64].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[7], e[8], e[15], e[16], e[19], e[21], e[23], e[24], e[25], e[27], e[28], 
# e[29], e[30], e[31], e[32], e[38], e[39], e[44], e[46], e[57], e[59], e[62], e[64]]
# where e is the list of the elements of the group [64,11] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,11));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 11]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,11] is 522
### The list of all inequivalent (64,28,12) DSs in group [64,11] is 
  
  
DS11:=[ [ 1, 2, 3, 4, 5, 7, 8, 15, 16, 19, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 38, 39, 44, 46, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 16, 19, 20, 21, 29, 31, 34, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 16, 19, 20, 21, 25, 30, 31, 32, 34, 42, 45, 47, 49, 50, 51, 55, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 16, 19, 20, 21, 23, 24, 25, 30, 31, 32, 34, 42, 44, 46, 49, 50, 51, 55, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 15, 16, 19, 21, 25, 30, 31, 32, 38, 39, 45, 47, 49, 50, 51, 57, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 15, 16, 19, 21, 23, 24, 25, 30, 31, 32, 38, 39, 44, 46, 49, 50, 51, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 14, 15, 19, 21, 24, 32, 33, 35, 36, 39, 44, 45, 46, 47, 48, 51, 53, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 14, 15, 19, 21, 23, 24, 32, 33, 35, 36, 39, 46, 47, 48, 51, 53, 55, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 13, 15, 19, 21, 32, 33, 34, 37, 39, 43, 44, 45, 48, 51, 53, 56, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 13, 15, 19, 21, 23, 32, 33, 34, 37, 39, 43, 48, 51, 53, 56, 57, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 19, 21, 24, 25, 26, 28, 34, 35, 38, 39, 46, 48, 53, 54, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 19, 21, 24, 25, 26, 28, 34, 35, 38, 39, 43, 46, 48, 53, 54, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 19, 21, 24, 25, 26, 28, 33, 38, 39, 46, 48, 55, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 19, 21, 24, 25, 26, 28, 33, 38, 39, 43, 46, 48, 55, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 15, 16, 19, 21, 25, 27, 32, 38, 39, 45, 47, 51, 52, 57, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 15, 16, 19, 21, 24, 25, 27, 32, 38, 39, 43, 45, 46, 51, 52, 57, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 15, 16, 19, 21, 23, 24, 25, 27, 32, 38, 39, 44, 46, 51, 52, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 15, 19, 21, 30, 31, 32, 33, 35, 36, 39, 44, 45, 48, 51, 52, 53, 55, 57 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 15, 19, 21, 23, 30, 31, 32, 33, 35, 36, 39, 48, 51, 52, 53, 55, 57, 60 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 15, 19, 21, 30, 31, 32, 33, 34, 37, 39, 44, 45, 48, 51, 52, 53, 56, 57 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 15, 19, 21, 23, 30, 31, 32, 33, 34, 37, 39, 48, 51, 52, 53, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 12, 18, 20, 24, 27, 31, 32, 33, 34, 35, 36, 37, 38, 40, 47, 50, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 16, 18, 20, 24, 27, 32, 33, 35, 36, 40, 52, 54, 56, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 16, 18, 20, 24, 27, 32, 33, 35, 36, 40, 43, 52, 54, 56, 57, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 16, 18, 20, 24, 27, 32, 35, 37, 40, 52, 53, 57, 58, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 16, 18, 20, 24, 27, 32, 35, 37, 40, 43, 52, 53, 57, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 20, 24, 27, 29, 34, 35, 38, 40, 47, 49, 50, 53, 54, 56, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 24, 27, 29, 33, 38, 40, 47, 49, 50, 55, 56, 57, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 16, 19, 21, 23, 27, 30, 32, 33, 36, 40, 44, 45, 49, 51, 55, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 14, 18, 20, 24, 29, 30, 31, 34, 35, 38, 40, 47, 52, 53, 54, 56, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 20, 24, 29, 31, 33, 38, 40, 46, 47, 49, 55, 56, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 18, 20, 24, 29, 30, 31, 33, 38, 40, 47, 52, 55, 56, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 19, 21, 28, 33, 37, 40, 43, 49, 50, 52, 55, 57, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 13, 14, 16, 19, 21, 27, 28, 37, 40, 43, 52, 53, 54, 55, 57, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 15, 16, 18, 20, 23, 26, 27, 28, 29, 30, 31, 32, 38, 40, 43, 45, 46, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 15, 16, 18, 20, 23, 24, 26, 27, 28, 29, 30, 31, 32, 38, 40, 45, 47, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 16, 17, 19, 21, 23, 24, 29, 36, 39, 46, 47, 48, 51, 53, 54, 55, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 17, 19, 21, 23, 29, 37, 39, 43, 48, 51, 53, 54, 55, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 18, 20, 23, 24, 26, 32, 33, 34, 35, 36, 37, 38, 40, 45, 47, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 18, 20, 23, 24, 26, 32, 34, 35, 38, 40, 45, 47, 53, 54, 56, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 18, 20, 23, 24, 26, 32, 36, 37, 38, 40, 45, 47, 53, 54, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 23, 24, 26, 32, 33, 38, 40, 45, 47, 55, 56, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 19, 21, 24, 32, 37, 40, 44, 45, 46, 48, 53, 54, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 19, 21, 24, 32, 37, 40, 43, 44, 45, 46, 48, 53, 54, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 19, 21, 23, 24, 32, 37, 40, 46, 48, 53, 54, 55, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 19, 21, 23, 24, 32, 37, 40, 43, 46, 48, 53, 54, 55, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 15, 16, 18, 20, 23, 26, 28, 29, 32, 38, 40, 43, 45, 46, 49, 50, 52, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 15, 16, 18, 20, 23, 24, 26, 28, 29, 32, 38, 40, 45, 47, 49, 50, 52, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 18, 20, 23, 26, 31, 32, 33, 34, 35, 36, 37, 38, 40, 45, 49, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 18, 20, 23, 26, 31, 32, 36, 37, 38, 40, 45, 49, 53, 54, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 16, 18, 20, 23, 26, 30, 31, 32, 38, 40, 43, 45, 46, 49, 50, 51, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 16, 18, 20, 23, 26, 29, 30, 31, 32, 38, 40, 46, 49, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 16, 18, 20, 23, 26, 27, 29, 30, 31, 32, 38, 40, 46, 50, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 16, 18, 20, 23, 24, 26, 30, 31, 32, 38, 40, 45, 47, 49, 50, 51, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 16, 17, 18, 21, 25, 26, 30, 31, 32, 33, 34, 36, 40, 48, 49, 50, 51, 53, 55 ], [ 1, 2, 3, 4, 5, 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33, 44, 46, 47, 49, 50, 52, 53, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 26, 27, 31, 33, 44, 45, 46, 51, 53, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 26, 27, 29, 33, 43, 44, 46, 47, 52, 53, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 29, 31, 33, 44, 45, 48, 49, 53, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 27, 31, 33, 44, 48, 51, 53, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 27, 31, 33, 43, 44, 48, 51, 53, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 26, 31, 33, 43, 44, 45, 47, 49, 50, 51, 53, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 26, 29, 33, 44, 49, 50, 52, 53, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 26, 29, 33, 43, 44, 49, 50, 52, 53, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 26, 27, 31, 33, 44, 45, 47, 51, 53, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 26, 27, 29, 33, 44, 52, 53, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 24, 26, 27, 29, 33, 43, 44, 52, 53, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 31, 33, 45, 46, 47, 48, 49, 50, 51, 53, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 31, 33, 43, 45, 46, 47, 48, 49, 50, 51, 53, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 29, 31, 33, 46, 47, 48, 49, 53, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 26, 31, 33, 46, 49, 50, 51, 53, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 26, 27, 31, 33, 43, 46, 51, 53, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 24, 29, 31, 33, 43, 48, 49, 53, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 24, 27, 31, 33, 45, 48, 51, 53, 58, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 24, 27, 31, 33, 43, 45, 48, 51, 53, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 24, 26, 31, 33, 47, 49, 50, 51, 53, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 24, 26, 27, 31, 33, 43, 47, 51, 53, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 22, 29, 31, 33, 35, 36, 41, 42, 43, 48, 49, 53, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 18, 20, 22, 26, 33, 34, 37, 38, 49, 51, 52, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 18, 20, 22, 26, 33, 34, 37, 38, 43, 49, 51, 52, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 18, 20, 22, 26, 27, 33, 34, 37, 38, 50, 51, 52, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 18, 20, 22, 26, 27, 33, 34, 37, 38, 43, 50, 51, 52, 56, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 26, 33, 36, 37, 49, 51, 52, 53, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 26, 33, 36, 37, 43, 49, 51, 52, 53, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 26, 27, 33, 36, 37, 50, 51, 52, 53, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 26, 27, 33, 36, 37, 43, 50, 51, 52, 53, 55, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 22, 29, 31, 34, 36, 41, 42, 43, 48, 49, 54, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 28, 30, 43, 44, 45, 46, 47, 48, 50, 53, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 28, 30, 33, 43, 44, 45, 46, 47, 48, 50, 54, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 28, 30, 44, 45, 48, 50, 53, 58, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 28, 30, 33, 44, 45, 48, 50, 54, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 28, 30, 46, 47, 48, 50, 53, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 28, 30, 33, 46, 47, 48, 50, 54, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 28, 30, 43, 48, 50, 53, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 28, 30, 33, 43, 48, 50, 54, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 22, 25, 33, 35, 36, 38, 43, 50, 51, 52, 56, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 22, 25, 27, 33, 35, 36, 38, 49, 51, 52, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 22, 28, 30, 33, 35, 36, 41, 42, 43, 48, 50, 54, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 25, 36, 37, 43, 50, 51, 52, 53, 55, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 25, 33, 36, 37, 43, 50, 51, 52, 54, 55, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 25, 27, 36, 37, 49, 51, 52, 53, 55, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 25, 27, 33, 36, 37, 49, 51, 52, 54, 55, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 21, 22, 25, 33, 35, 37, 38, 43, 50, 51, 52, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 21, 22, 25, 27, 33, 35, 37, 38, 49, 51, 52, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 28, 30, 35, 37, 41, 42, 43, 48, 50, 53, 62, 63, 64 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 195
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS11[8], DS11[16], DS11[21], DS11[29], DS11[31], DS11[33], DS11[34], DS11[37], DS11[38], DS11[43], DS11[44], DS11[45], DS11[46], DS11[48], DS11[52], DS11[56], DS11[67], DS11[68], DS11[81], DS11[82], DS11[83], DS11[84], DS11[85], DS11[86], DS11[89], DS11[91], DS11[98], DS11[99], DS11[100], DS11[101], DS11[102], DS11[103], DS11[104], DS11[105], DS11[106], DS11[107], DS11[108], DS11[109], DS11[116], DS11[120], DS11[126], DS11[132], DS11[134], DS11[135], DS11[138], DS11[139], DS11[141], DS11[144], DS11[145], DS11[147], DS11[153], DS11[155], DS11[161], DS11[164], DS11[168], DS11[170], DS11[171], DS11[176], DS11[178], DS11[179], DS11[183], DS11[184], DS11[185], DS11[187], DS11[188], DS11[189], DS11[192], DS11[193], DS11[202], DS11[203], DS11[204], DS11[208], DS11[209], DS11[212], DS11[213], DS11[217], DS11[218], DS11[219], DS11[220], DS11[221], DS11[222], DS11[223], DS11[224], DS11[225], DS11[226], DS11[227], DS11[229], DS11[230], DS11[231], DS11[232], DS11[234], DS11[237], DS11[238], DS11[240], DS11[244], DS11[258], DS11[262], DS11[265], DS11[266], DS11[269], DS11[274], DS11[276], DS11[281], DS11[282], DS11[287], DS11[289], DS11[292], DS11[294], DS11[295], DS11[296], DS11[297], DS11[298], DS11[299], DS11[300], DS11[301], DS11[302], DS11[321], DS11[323], DS11[324], DS11[325], DS11[326], DS11[327], DS11[331], DS11[332], DS11[333], DS11[334], DS11[335], DS11[336], DS11[343], DS11[345], DS11[349], DS11[363], DS11[364], DS11[375], DS11[376], DS11[377], DS11[378], DS11[392], DS11[396], DS11[397], DS11[403], DS11[404], DS11[406], DS11[407], DS11[408], DS11[410], DS11[411], DS11[412], DS11[413], DS11[421], DS11[423], DS11[425], DS11[426], DS11[438], DS11[439], DS11[453], DS11[454], DS11[455], DS11[456], DS11[457], DS11[458], DS11[459], DS11[460], DS11[461], DS11[462], DS11[463], DS11[464], DS11[465], DS11[466], DS11[467], DS11[468], DS11[475], DS11[479], DS11[484], DS11[485], DS11[489], DS11[494], DS11[495], DS11[496], DS11[497], DS11[498], DS11[499], DS11[500], DS11[501], DS11[502], DS11[503], DS11[504], DS11[513], DS11[514], DS11[516], DS11[517], DS11[518], DS11[519], DS11[520], DS11[521]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,11].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,11] is 10
### The list of all inequivalent reversible (64,28,12) DSs in group [64,11] is 
  
  
RDS11:=[ [ 2, 3, 5, 8, 9, 12, 15, 20, 21, 24, 26, 30, 35, 36, 37, 42, 43, 45, 46, 49, 50, 51, 52, 53, 54, 55, 59, 60 ], [ 2, 3, 5, 8, 9, 12, 14, 15, 20, 21, 24, 26, 30, 33, 35, 42, 43, 45, 46, 49, 50, 51, 52, 55, 56, 59, 60, 63 ], [ 2, 3, 5, 8, 9, 12, 13, 14, 15, 20, 21, 24, 25, 30, 33, 34, 42, 43, 44, 47, 49, 50, 51, 52, 56, 58, 60, 63 ], [ 2, 3, 5, 8, 9, 12, 13, 14, 15, 20, 21, 23, 25, 30, 33, 34, 42, 43, 45, 46, 49, 50, 51, 52, 56, 58, 61, 63 ], [ 2, 3, 4, 8, 9, 12, 15, 18, 19, 24, 26, 30, 35, 36, 37, 41, 43, 45, 46, 49, 50, 51, 52, 53, 54, 55, 59, 60 ], [ 2, 3, 4, 8, 9, 12, 13, 14, 15, 18, 19, 24, 25, 30, 33, 34, 41, 43, 44, 47, 49, 50, 51, 52, 56, 58, 60, 63 ], [ 2, 3, 4, 8, 9, 12, 13, 14, 15, 18, 19, 23, 25, 30, 33, 34, 41, 43, 45, 46, 49, 50, 51, 52, 56, 58, 61, 63 ], [ 1, 2, 3, 6, 7, 8, 9, 12, 15, 22, 24, 26, 30, 35, 36, 37, 43, 45, 46, 49, 50, 51, 52, 53, 54, 55, 59, 60 ], [ 1, 2, 3, 6, 7, 8, 9, 12, 13, 14, 15, 22, 24, 25, 30, 33, 34, 43, 44, 47, 49, 50, 51, 52, 56, 58, 60, 63 ], [ 1, 2, 3, 6, 7, 8, 9, 12, 13, 14, 15, 22, 23, 25, 30, 33, 34, 43, 45, 46, 49, 50, 51, 52, 56, 58, 61, 63 ] ];
  
  
  
   
   
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