### 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 [64,135]. 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 [64,135].
    
    
# 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(64,135));' can be 
# used to create a list e of the elements of the group [64,135].
# In our list of (64,28,12) DSs in group [64,135], we have [1, 
# 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 19, 20, 27, 32, 
# 33, 35, 38, 39, 45, 51, 54, 56, 57, 59, 60, 62, 64].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[6], e[9], e[11], e[12], e[13], e[14], e[19], e[20], e[27], e[32], e[33], 
# e[35], e[38], e[39], e[45], e[51], e[54], e[56], e[57], e[59], e[60], e[62], e[64]]
# where e is the list of the elements of the group [64,135] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,135));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 135]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,135] is 540
### The list of all inequivalent (64,28,12) DSs in group [64,135] is 
  
  
DS135:=[ [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 19, 20, 27, 32, 33, 35, 38, 39, 45, 51, 54, 56, 57, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 19, 20, 23, 32, 33, 35, 38, 39, 44, 49, 50, 51, 54, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 19, 20, 27, 32, 33, 35, 36, 39, 43, 44, 45, 51, 54, 57, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 19, 20, 23, 32, 33, 35, 36, 39, 43, 49, 50, 51, 54, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 16, 17, 20, 24, 26, 29, 30, 31, 32, 34, 35, 36, 41, 47, 50, 51, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 18, 19, 20, 23, 25, 30, 31, 32, 35, 38, 41, 43, 45, 47, 53, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 17, 19, 20, 25, 27, 28, 30, 31, 32, 34, 35, 38, 40, 47, 50, 51, 55, 56, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 17, 18, 24, 26, 34, 35, 36, 38, 42, 43, 46, 47, 49, 54, 57, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 24, 26, 27, 30, 34, 35, 39, 41, 42, 47, 49, 50, 52, 54, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 24, 25, 26, 27, 34, 35, 39, 41, 42, 44, 47, 48, 50, 54, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 23, 26, 27, 34, 35, 39, 41, 42, 44, 45, 50, 54, 56, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 23, 25, 26, 27, 34, 35, 39, 41, 42, 45, 46, 48, 50, 54, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 23, 25, 26, 27, 35, 42, 45, 46, 48, 50, 53, 54, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 15, 17, 18, 23, 26, 34, 36, 37, 42, 43, 44, 45, 49, 53, 54, 57, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 24, 26, 36, 38, 39, 40, 42, 43, 46, 47, 49, 54, 55, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 24, 26, 27, 30, 36, 38, 39, 40, 42, 47, 49, 50, 52, 54, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 25, 26, 28, 30, 33, 34, 36, 38, 39, 41, 42, 48, 49, 51, 52, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 24, 26, 27, 30, 33, 34, 36, 38, 39, 41, 42, 47, 49, 50, 52, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 24, 25, 26, 28, 33, 34, 36, 38, 39, 41, 42, 43, 47, 48, 51, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 23, 26, 27, 28, 33, 34, 36, 38, 39, 41, 42, 45, 49, 50, 51, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 23, 25, 26, 30, 33, 34, 36, 38, 39, 41, 42, 43, 45, 48, 52, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 18, 25, 26, 28, 33, 36, 38, 42, 46, 48, 51, 53, 55, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 18, 25, 26, 28, 30, 33, 36, 38, 42, 48, 49, 51, 52, 53, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 18, 24, 26, 33, 36, 38, 42, 43, 46, 47, 49, 53, 55, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 18, 24, 25, 26, 28, 33, 36, 38, 42, 43, 47, 48, 51, 53, 55, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 17, 18, 23, 26, 28, 33, 36, 38, 42, 43, 45, 51, 53, 55, 57, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 15, 17, 23, 26, 27, 30, 32, 33, 34, 35, 36, 37, 39, 41, 42, 45, 50, 52, 53 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 26, 28, 32, 33, 35, 36, 38, 40, 41, 42, 46, 49, 51, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 23, 26, 32, 33, 35, 36, 38, 40, 41, 42, 43, 45, 46, 55, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 17, 24, 26, 27, 28, 32, 35, 36, 38, 39, 41, 42, 47, 50, 51, 53, 54, 55 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 17, 23, 26, 27, 30, 32, 35, 36, 38, 39, 41, 42, 45, 50, 52, 53, 54, 55 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 15, 17, 24, 26, 32, 34, 35, 39, 41, 42, 43, 44, 47, 54, 56, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 15, 17, 24, 26, 27, 28, 32, 34, 35, 39, 41, 42, 47, 50, 51, 54, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 15, 26, 28, 32, 33, 36, 37, 40, 41, 42, 46, 49, 51, 53, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 24, 26, 27, 28, 32, 36, 38, 39, 40, 42, 47, 50, 51, 54, 55, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 23, 26, 32, 36, 38, 39, 40, 42, 43, 45, 46, 54, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 23, 24, 26, 32, 36, 38, 39, 40, 42, 45, 47, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 26, 28, 32, 33, 34, 36, 38, 39, 41, 42, 46, 49, 51, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 26, 28, 30, 32, 33, 34, 36, 38, 39, 41, 42, 51, 52, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 24, 26, 27, 28, 32, 33, 34, 36, 38, 39, 41, 42, 47, 50, 51, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 23, 26, 27, 30, 32, 33, 34, 36, 38, 39, 41, 42, 45, 50, 52, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 23, 24, 26, 32, 33, 34, 36, 38, 39, 41, 42, 45, 47, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 17, 18, 24, 26, 32, 33, 36, 38, 42, 43, 44, 47, 53, 55, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 17, 25, 26, 27, 28, 31, 35, 36, 38, 39, 41, 42, 48, 50, 51, 53, 54, 55 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 17, 18, 26, 31, 34, 35, 36, 38, 42, 43, 46, 54, 57, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 17, 18, 26, 27, 31, 34, 35, 36, 38, 42, 46, 49, 50, 54, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 17, 18, 23, 25, 26, 31, 34, 35, 36, 38, 42, 45, 48, 54, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 17, 25, 26, 27, 28, 31, 34, 35, 39, 41, 42, 48, 50, 51, 54, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 17, 23, 26, 31, 34, 35, 39, 41, 42, 44, 45, 46, 54, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 17, 23, 25, 26, 31, 34, 35, 39, 41, 42, 45, 48, 54, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 17, 18, 26, 27, 31, 35, 42, 46, 49, 50, 53, 54, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 17, 18, 26, 27, 31, 34, 36, 37, 42, 46, 49, 50, 53, 54, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 17, 18, 25, 26, 31, 34, 36, 37, 42, 43, 44, 48, 53, 54, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 17, 18, 25, 26, 27, 28, 31, 34, 36, 37, 42, 48, 50, 51, 53, 54, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 17, 18, 23, 26, 31, 34, 36, 37, 42, 44, 45, 46, 53, 54, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 20, 25, 26, 27, 28, 31, 34, 38, 39, 40, 41, 48, 50, 51, 54, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 26, 31, 36, 38, 39, 40, 42, 43, 46, 54, 55, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 25, 26, 27, 28, 31, 36, 38, 39, 40, 42, 48, 50, 51, 54, 55, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 17, 25, 26, 27, 28, 31, 33, 34, 36, 38, 39, 41, 42, 48, 50, 51, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 17, 18, 26, 31, 33, 36, 38, 42, 43, 46, 53, 55, 57, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 17, 18, 26, 27, 31, 33, 36, 38, 42, 46, 49, 50, 53, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 17, 18, 25, 26, 27, 28, 31, 33, 36, 38, 42, 48, 50, 51, 53, 55, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 17, 18, 23, 25, 26, 31, 33, 36, 38, 42, 45, 48, 53, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 26, 28, 31, 32, 35, 37, 38, 40, 41, 42, 43, 51, 53, 54, 55, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 26, 27, 31, 32, 35, 37, 38, 40, 41, 42, 44, 50, 53, 54, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 18, 26, 28, 31, 32, 34, 35, 37, 38, 39, 40, 42, 43, 51, 54, 56, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 18, 26, 27, 31, 32, 34, 35, 37, 38, 39, 40, 42, 44, 50, 54, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 26, 28, 31, 32, 34, 35, 36, 37, 40, 41, 42, 43, 51, 54, 57, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 26, 27, 31, 32, 34, 35, 36, 37, 40, 41, 42, 44, 50, 54, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 18, 26, 28, 31, 32, 35, 36, 37, 39, 40, 42, 43, 51, 53, 54, 55, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 18, 26, 27, 31, 32, 35, 36, 37, 39, 40, 42, 44, 50, 53, 54, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 17, 26, 28, 31, 32, 33, 34, 35, 36, 37, 39, 41, 42, 43, 51, 53, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 17, 26, 27, 31, 32, 33, 34, 35, 36, 37, 39, 41, 42, 44, 50, 53, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 14, 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24, 26, 29, 30, 33, 41, 44, 46, 49, 50, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 22, 23, 29, 30, 42, 43, 44, 46, 48, 49, 50, 53, 54, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 22, 23, 24, 29, 30, 42, 44, 47, 48, 49, 50, 53, 54, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 27, 31, 43, 44, 46, 47, 48, 51, 54, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 22, 23, 27, 31, 45, 46, 47, 48, 51, 54, 58, 62, 63, 64 ], [ 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, 26, 33, 43, 49, 51, 52, 53, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 22, 27, 31, 33, 34, 36, 43, 48, 51, 54, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 22, 25, 28, 31, 36, 41, 42, 43, 50, 53, 54, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 22, 25, 27, 28, 31, 33, 36, 41, 42, 43, 49, 55, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 18, 20, 22, 25, 27, 31, 36, 43, 51, 53, 54, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 18, 20, 22, 25, 27, 31, 35, 38, 51, 53, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 22, 27, 28, 31, 35, 36, 41, 42, 48, 49, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 22, 27, 31, 35, 36, 43, 48, 51, 53, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 24, 25, 29, 30, 33, 38, 41, 42, 44, 46, 49, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 24, 25, 27, 29, 31, 33, 38, 41, 42, 43, 44, 47, 49, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 24, 25, 27, 29, 30, 33, 38, 41, 42, 43, 44, 46, 50, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 25, 29, 31, 38, 41, 42, 43, 45, 46, 50, 53, 54, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 25, 29, 31, 33, 38, 41, 42, 45, 46, 50, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 25, 28, 31, 33, 38, 41, 42, 44, 46, 49, 58, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 25, 27, 29, 31, 33, 38, 41, 42, 43, 45, 46, 49, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 25, 27, 28, 31, 33, 38, 41, 42, 43, 44, 46, 50, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 24, 25, 29, 30, 33, 38, 41, 42, 43, 45, 46, 49, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 24, 25, 28, 31, 33, 38, 41, 42, 43, 44, 47, 49, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 24, 25, 27, 29, 30, 33, 38, 41, 42, 45, 46, 50, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 24, 25, 27, 28, 31, 33, 38, 41, 42, 44, 47, 50, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 22, 25, 27, 31, 38, 42, 43, 44, 45, 46, 50, 51, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 22, 24, 25, 31, 38, 42, 43, 44, 45, 47, 49, 51, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 22, 23, 25, 27, 31, 33, 38, 42, 43, 46, 50, 51, 53, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 22, 23, 24, 25, 31, 33, 38, 42, 43, 47, 49, 51, 53, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 22, 27, 29, 30, 35, 36, 41, 42, 48, 50, 54, 55, 56, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 43, 45, 46, 48, 50, 51, 52, 53, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 27, 30, 45, 48, 51, 53, 59, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 27, 28, 44, 45, 46, 48, 52, 53, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 25, 30, 43, 44, 45, 46, 49, 50, 51, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 25, 27, 44, 45, 49, 51, 52, 53, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 25, 43, 46, 47, 50, 51, 52, 53, 58, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 25, 27, 30, 47, 51, 53, 58, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 25, 27, 28, 44, 46, 47, 52, 53, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 30, 44, 48, 49, 50, 51, 53, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 28, 46, 48, 49, 50, 52, 53, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 27, 43, 44, 46, 48, 49, 51, 52, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 27, 28, 43, 46, 48, 52, 53, 58, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 27, 28, 31, 41, 42, 43, 44, 45, 46, 48, 50, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 26, 27, 29, 30, 41, 42, 44, 45, 46, 50, 54, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 26, 27, 28, 31, 33, 41, 42, 44, 46, 47, 50, 53, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 24, 28, 31, 41, 42, 43, 44, 45, 47, 48, 49, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 24, 26, 29, 30, 41, 42, 44, 45, 47, 49, 54, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 24, 26, 27, 29, 31, 41, 42, 44, 45, 49, 54, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 23, 26, 29, 31, 33, 41, 42, 46, 47, 50, 53, 58, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 23, 26, 28, 31, 33, 41, 42, 45, 46, 47, 49, 53, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 22, 26, 27, 31, 42, 43, 44, 46, 47, 50, 51, 53, 54, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 22, 26, 27, 31, 33, 42, 44, 46, 47, 50, 51, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 22, 23, 26, 31, 42, 43, 45, 46, 47, 49, 51, 53, 54, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 22, 23, 26, 31, 33, 42, 45, 46, 47, 49, 51, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 22, 25, 27, 29, 30, 33, 34, 38, 41, 42, 43, 50, 54, 55, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 19, 23, 25, 26, 32, 34, 40, 46, 47, 49, 50, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 24, 25, 29, 32, 40, 43, 44, 47, 48, 49, 51, 53, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 19, 23, 32, 33, 34, 35, 41, 49, 50, 53, 55, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 22, 29, 30, 35, 37, 41, 42, 48, 49, 54, 55, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 17, 19, 23, 32, 33, 35, 36, 38, 41, 49, 50, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 23, 28, 29, 32, 34, 36, 37, 40, 57, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 19, 29, 33, 41, 47, 48, 49, 52, 53, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 19, 23, 32, 37, 41, 46, 49, 50, 55, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 29, 33, 34, 47, 48, 49, 52, 53, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 22, 25, 27, 29, 30, 33, 36, 41, 42, 50, 55, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 22, 25, 29, 30, 33, 35, 38, 41, 42, 43, 49, 54, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 25, 29, 30, 33, 37, 41, 42, 49, 55, 59, 62, 63, 64 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 236
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS135[3], DS135[6], DS135[7], DS135[14], DS135[53], DS135[56], DS135[61], DS135[85], DS135[86], DS135[87], DS135[89], DS135[90], DS135[91], DS135[94], DS135[95], DS135[102], DS135[103], DS135[107], DS135[114], DS135[115], DS135[125], DS135[129], DS135[138], DS135[150], DS135[156], DS135[159], DS135[160], DS135[162], DS135[179], DS135[189], DS135[190], DS135[192], DS135[194], DS135[211], DS135[212], DS135[214], DS135[221], DS135[222], DS135[225], DS135[227], DS135[234], DS135[247], DS135[248], DS135[249], DS135[250], DS135[251], DS135[252], DS135[257], DS135[258], DS135[260], DS135[265], DS135[269], DS135[273], DS135[285], DS135[286], DS135[287], DS135[291], DS135[292], DS135[293], DS135[296], DS135[297], DS135[298], DS135[299], DS135[301], DS135[302], DS135[303], DS135[304], DS135[305], DS135[311], DS135[312], DS135[313], DS135[314], DS135[315], DS135[317], DS135[322], DS135[323], DS135[324], DS135[327], DS135[328], DS135[337], DS135[339], DS135[340], DS135[341], DS135[342], DS135[343], DS135[344], DS135[345], DS135[346], DS135[347], DS135[348], DS135[349], DS135[350], DS135[351], DS135[352], DS135[353], DS135[354], DS135[355], DS135[356], DS135[357], DS135[358], DS135[359], DS135[360], DS135[361], DS135[362], DS135[363], DS135[364], DS135[365], DS135[366], DS135[367], DS135[368], DS135[369], DS135[370], DS135[371], DS135[374], DS135[376], DS135[379], DS135[380], DS135[388], DS135[391], DS135[392], DS135[393], DS135[394], DS135[395], DS135[396], DS135[397], DS135[398], DS135[399], DS135[400], DS135[401], DS135[402], DS135[403], DS135[404], DS135[416], DS135[421], DS135[422], DS135[423], DS135[424], DS135[425], DS135[426], DS135[427], DS135[428], DS135[429], DS135[430], DS135[431], DS135[432], DS135[433], DS135[434], DS135[435], DS135[436], DS135[437], DS135[438], DS135[439], DS135[440], DS135[441], DS135[442], DS135[443], DS135[444], DS135[445], DS135[446], DS135[447], DS135[448], DS135[449], DS135[450], DS135[451], DS135[452], DS135[454], DS135[457], DS135[458], DS135[460], DS135[461], DS135[462], DS135[463], DS135[464], DS135[465], DS135[466], DS135[467], DS135[468], DS135[469], DS135[470], DS135[471], DS135[472], DS135[473], DS135[474], DS135[476], DS135[477], DS135[478], DS135[479], DS135[480], DS135[481], DS135[482], DS135[483], DS135[484], DS135[485], DS135[486], DS135[487], DS135[489], DS135[490], DS135[491], DS135[492], DS135[494], DS135[495], DS135[496], DS135[497], DS135[498], DS135[499], DS135[500], DS135[501], DS135[502], DS135[503], DS135[507], DS135[510], DS135[512], DS135[516], DS135[517], DS135[518], DS135[519], DS135[520], DS135[522], DS135[523], DS135[524], DS135[525], DS135[526], DS135[527], DS135[528], DS135[529], DS135[530], DS135[531], DS135[532], DS135[533], DS135[534], DS135[535], DS135[536], DS135[537], DS135[538], DS135[539], DS135[540]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,135].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,135] is 448
### The list of all inequivalent reversible (64,28,12) DSs in group [64,135] is 
  
  
RDS135:=[ [ 2, 5, 8, 9, 10, 11, 13, 15, 20, 21, 24, 25, 27, 35, 36, 38, 42, 44, 45, 49, 51, 52, 53, 56, 59, 61, 63, 64 ], [ 2, 4, 8, 9, 10, 13, 15, 18, 19, 23, 24, 25, 30, 32, 35, 36, 38, 41, 44, 50, 51, 53, 56, 58, 59, 61, 62, 63 ], [ 2, 4, 8, 9, 10, 11, 13, 15, 18, 19, 24, 25, 27, 35, 36, 38, 41, 44, 45, 49, 51, 52, 53, 56, 59, 61, 63, 64 ], [ 2, 4, 6, 8, 9, 10, 15, 17, 18, 19, 22, 23, 24, 25, 30, 32, 38, 40, 41, 44, 50, 51, 53, 58, 59, 61, 62, 63 ], [ 2, 4, 6, 8, 9, 10, 11, 17, 19, 22, 24, 25, 27, 36, 39, 40, 44, 45, 49, 51, 52, 53, 56, 57, 59, 61, 63, 64 ], [ 2, 4, 6, 8, 9, 10, 11, 13, 18, 19, 22, 24, 35, 36, 39, 41, 43, 45, 46, 48, 50, 51, 52, 56, 57, 60, 62, 64 ], [ 2, 4, 6, 8, 9, 10, 11, 13, 18, 19, 22, 24, 25, 27, 35, 36, 39, 41, 44, 45, 49, 51, 52, 56, 57, 59, 61, 64 ], [ 2, 4, 5, 8, 9, 10, 13, 17, 19, 20, 21, 24, 27, 30, 32, 35, 40, 42, 44, 45, 46, 48, 49, 51, 53, 59, 63, 64 ], [ 2, 4, 5, 8, 9, 10, 13, 17, 19, 20, 21, 23, 24, 25, 30, 32, 35, 40, 42, 44, 50, 51, 53, 58, 59, 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