### 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 [64,126]. 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 [64,126].
    
    
# 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(64,126));' can be 
# used to create a list e of the elements of the group [64,126].
# In our list of (64,28,12) DSs in group [64,126], we have [1, 
# 2, 3, 4, 5, 7, 8, 9, 13, 15, 16, 17, 18, 21, 24, 
# 29, 30, 31, 32, 38, 39, 48, 49, 53, 54, 55, 61, 62].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[7], e[8], e[9], e[13], e[15], e[16], e[17], e[18], e[21], e[24], e[29], 
# e[30], e[31], e[32], e[38], e[39], e[48], e[49], e[53], e[54], e[55], e[61], e[62]]
# where e is the list of the elements of the group [64,126] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,126));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 126]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,126] is 572
### The list of all inequivalent (64,28,12) DSs in group [64,126] is 
  
  
DS126:=[ [ 1, 2, 3, 4, 5, 7, 8, 9, 13, 15, 16, 17, 18, 21, 24, 29, 30, 31, 32, 38, 39, 48, 49, 53, 54, 55, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 18, 21, 24, 29, 31, 34, 38, 39, 48, 49, 52, 54, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 17, 18, 21, 24, 28, 32, 35, 36, 37, 38, 39, 48, 50, 53, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18, 21, 24, 32, 35, 37, 39, 48, 49, 50, 51, 53, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 19, 20, 23, 25, 30, 38, 41, 46, 48, 49, 50, 51, 52, 56, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 19, 20, 23, 25, 28, 30, 38, 41, 44, 46, 48, 50, 52, 56, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 14, 18, 20, 23, 25, 29, 31, 38, 40, 44, 45, 46, 48, 49, 52, 56, 57, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 14, 18, 20, 23, 25, 28, 29, 31, 38, 40, 45, 46, 48, 51, 52, 56, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 19, 20, 23, 25, 32, 38, 39, 46, 48, 49, 50, 51, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 19, 20, 23, 25, 28, 32, 38, 39, 44, 46, 48, 50, 56, 57, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 19, 20, 22, 28, 30, 41, 42, 46, 47, 48, 49, 52, 53, 54, 55, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 18, 19, 20, 22, 25, 28, 31, 35, 41, 42, 47, 49, 52, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 20, 22, 26, 28, 32, 39, 40, 41, 42, 46, 49, 53, 54, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 19, 20, 22, 28, 32, 39, 42, 46, 47, 48, 49, 53, 54, 55, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 19, 20, 22, 25, 28, 32, 34, 39, 42, 47, 49, 54, 57, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 20, 22, 25, 28, 32, 35, 40, 42, 47, 49, 53, 57, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 19, 20, 22, 26, 34, 35, 42, 44, 46, 48, 51, 52, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 19, 20, 22, 26, 28, 35, 42, 46, 48, 49, 52, 53, 55, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 19, 20, 22, 25, 26, 28, 35, 42, 49, 52, 53, 55, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 18, 19, 20, 22, 25, 26, 28, 34, 35, 42, 49, 52, 57, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 18, 20, 29, 31, 38, 39, 40, 41, 43, 47, 49, 54, 56, 57, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 18, 20, 28, 29, 31, 38, 39, 40, 41, 43, 44, 47, 51, 54, 56, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 18, 20, 23, 29, 31, 38, 39, 40, 41, 44, 45, 47, 49, 54, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 18, 20, 23, 28, 29, 31, 38, 39, 40, 41, 45, 47, 51, 54, 56, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 18, 20, 25, 28, 29, 30, 38, 40, 44, 47, 51, 52, 56, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 18, 20, 25, 26, 27, 29, 30, 33, 35, 38, 40, 48, 50, 52, 53, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 16, 20, 23, 28, 29, 30, 37, 39, 40, 41, 43, 44, 46, 47, 48, 51, 52, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 14, 16, 20, 23, 27, 28, 30, 37, 39, 40, 41, 44, 45, 46, 47, 48, 49, 52, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 18, 20, 25, 26, 27, 29, 30, 34, 38, 40, 48, 50, 52, 54, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 18, 19, 20, 23, 26, 35, 38, 39, 41, 49, 50, 51, 56, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 18, 19, 20, 23, 26, 28, 35, 38, 39, 41, 44, 50, 56, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 16, 17, 19, 20, 23, 25, 27, 28, 31, 36, 40, 44, 45, 47, 49, 52, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 19, 20, 25, 27, 28, 31, 38, 39, 44, 47, 49, 52, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 18, 20, 26, 27, 28, 31, 38, 40, 44, 46, 49, 52, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 18, 20, 23, 26, 27, 29, 31, 38, 40, 43, 44, 46, 50, 52, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 18, 20, 23, 26, 27, 28, 31, 38, 40, 43, 45, 46, 49, 52, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 15, 16, 17, 19, 20, 23, 25, 27, 28, 31, 38, 40, 45, 47, 49, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 19, 20, 25, 28, 29, 31, 38, 39, 44, 47, 51, 52, 56, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 19, 20, 23, 25, 27, 29, 31, 38, 39, 44, 45, 47, 50, 52, 56, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 18, 20, 26, 28, 29, 31, 38, 40, 44, 46, 51, 52, 56, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 18, 20, 23, 26, 28, 29, 31, 38, 40, 43, 45, 46, 51, 52, 56, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 18, 20, 23, 26, 27, 29, 31, 38, 40, 44, 45, 46, 50, 52, 56, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 18, 19, 20, 25, 29, 31, 38, 41, 44, 47, 49, 52, 56, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 18, 19, 20, 23, 25, 27, 29, 31, 38, 41, 45, 47, 50, 52, 56, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 17, 19, 20, 25, 28, 29, 31, 38, 40, 43, 44, 47, 51, 52, 56, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 17, 19, 20, 23, 25, 28, 29, 31, 38, 40, 45, 47, 51, 52, 56, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 18, 20, 25, 26, 27, 28, 31, 33, 34, 37, 40, 48, 49, 52, 54, 55, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 18, 20, 23, 26, 28, 29, 31, 37, 40, 43, 44, 46, 51, 52, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 18, 20, 23, 26, 27, 28, 31, 37, 40, 44, 45, 46, 49, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 16, 20, 28, 29, 30, 31, 32, 36, 40, 45, 47, 51, 52, 54, 56, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 16, 20, 27, 28, 30, 31, 32, 36, 40, 43, 47, 49, 52, 54, 56, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 16, 20, 23, 28, 29, 30, 31, 32, 36, 40, 43, 44, 47, 51, 52, 54, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 16, 20, 23, 27, 28, 30, 31, 32, 36, 40, 44, 45, 47, 49, 52, 54, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 20, 29, 30, 31, 32, 38, 40, 45, 47, 49, 52, 54, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 20, 27, 28, 30, 31, 32, 38, 40, 43, 44, 47, 49, 52, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 20, 23, 29, 30, 31, 32, 38, 40, 43, 44, 47, 49, 52, 54, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 20, 23, 27, 28, 30, 31, 32, 38, 40, 45, 47, 49, 52, 54, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 18, 20, 24, 26, 27, 28, 31, 35, 38, 40, 47, 49, 52, 53, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 17, 19, 20, 25, 27, 28, 31, 35, 38, 40, 47, 49, 52, 53, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 22, 27, 30, 31, 32, 36, 40, 45, 47, 49, 52, 54, 56, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 22, 27, 30, 31, 32, 36, 40, 44, 45, 47, 49, 52, 54, 56, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 22, 27, 28, 30, 31, 32, 36, 40, 45, 47, 51, 52, 54, 56, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 22, 27, 28, 30, 31, 32, 36, 40, 44, 45, 47, 51, 52, 54, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 20, 29, 30, 31, 32, 38, 40, 43, 47, 49, 52, 54, 56, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 20, 28, 29, 30, 31, 32, 38, 40, 43, 44, 47, 51, 52, 54, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 20, 23, 29, 30, 31, 32, 38, 40, 44, 45, 47, 49, 52, 54, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 20, 23, 28, 29, 30, 31, 32, 38, 40, 45, 47, 51, 52, 54, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 19, 20, 24, 26, 28, 29, 31, 34, 38, 39, 47, 51, 52, 54, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 18, 20, 25, 26, 27, 29, 31, 35, 38, 40, 48, 50, 52, 53, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 18, 20, 24, 26, 28, 29, 31, 35, 38, 40, 47, 51, 52, 53, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 18, 19, 20, 24, 26, 29, 31, 34, 38, 41, 47, 49, 52, 54, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 17, 19, 20, 26, 28, 29, 31, 34, 38, 40, 46, 51, 52, 54, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 17, 19, 20, 25, 28, 29, 31, 35, 38, 40, 47, 51, 52, 53, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 17, 19, 20, 25, 26, 29, 31, 34, 38, 40, 48, 49, 52, 54, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 16, 19, 20, 25, 26, 27, 28, 31, 34, 37, 39, 48, 49, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 16, 18, 20, 25, 26, 27, 28, 31, 35, 37, 40, 48, 49, 52, 53, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 29, 30, 31, 32, 38, 40, 43, 44, 47, 51, 52, 54, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 28, 29, 30, 31, 32, 38, 40, 43, 47, 49, 52, 54, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 27, 30, 31, 32, 38, 40, 45, 47, 49, 52, 54, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 27, 30, 31, 32, 38, 40, 44, 45, 47, 49, 52, 54, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 27, 28, 30, 31, 32, 38, 40, 45, 47, 51, 52, 54, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 27, 28, 30, 31, 32, 38, 40, 44, 45, 47, 51, 52, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 23, 29, 30, 31, 32, 38, 40, 44, 45, 47, 51, 52, 54, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 22, 23, 28, 29, 30, 31, 32, 38, 40, 45, 47, 49, 52, 54, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 17, 19, 20, 23, 26, 28, 32, 36, 37, 38, 40, 43, 44, 46, 50, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 17, 19, 20, 23, 26, 27, 28, 32, 36, 37, 38, 40, 44, 46, 49, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20, 23, 27, 29, 32, 36, 39, 40, 41, 43, 44, 46, 47, 48, 50, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 18, 20, 25, 27, 28, 32, 36, 40, 44, 47, 49, 56, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 18, 20, 23, 25, 27, 29, 32, 36, 40, 43, 44, 47, 50, 56, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 18, 20, 23, 25, 27, 28, 32, 36, 40, 43, 45, 47, 49, 56, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 20, 23, 26, 32, 37, 40, 43, 44, 46, 49, 50, 51, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 15, 17, 19, 20, 23, 26, 27, 28, 32, 37, 40, 46, 49, 56, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 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### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 335
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS126[1], DS126[13], DS126[17], DS126[18], DS126[20], DS126[25], DS126[27], DS126[28], DS126[37], DS126[39], DS126[41], DS126[43], DS126[54], DS126[55], DS126[56], DS126[57], DS126[58], DS126[60], DS126[62], DS126[77], DS126[78], DS126[79], DS126[81], DS126[83], DS126[84], DS126[90], DS126[94], DS126[96], DS126[97], DS126[112], DS126[120], DS126[124], DS126[126], DS126[128], DS126[133], DS126[134], DS126[135], DS126[136], DS126[137], DS126[138], DS126[146], DS126[147], DS126[152], DS126[153], DS126[160], DS126[162], DS126[165], DS126[166], DS126[167], DS126[171], DS126[172], DS126[174], DS126[175], DS126[177], DS126[179], DS126[181], DS126[182], DS126[183], DS126[184], DS126[187], DS126[191], DS126[198], DS126[202], DS126[203], DS126[212], DS126[216], DS126[217], DS126[227], DS126[228], DS126[229], DS126[230], DS126[232], DS126[236], DS126[237], DS126[240], DS126[241], DS126[242], DS126[243], DS126[244], DS126[245], DS126[253], DS126[254], DS126[255], DS126[256], DS126[257], DS126[258], DS126[259], DS126[260], DS126[261], DS126[262], DS126[263], DS126[264], DS126[265], DS126[269], DS126[270], DS126[271], DS126[272], DS126[273], DS126[274], DS126[275], DS126[276], DS126[278], DS126[281], DS126[282], DS126[285], DS126[286], DS126[287], DS126[288], DS126[289], DS126[290], DS126[291], DS126[292], DS126[295], DS126[298], DS126[299], DS126[300], DS126[309], DS126[312], DS126[317], DS126[318], DS126[319], DS126[320], DS126[321], DS126[322], DS126[323], DS126[324], DS126[325], DS126[326], DS126[327], DS126[328], DS126[330], DS126[331], DS126[335], DS126[336], DS126[337], DS126[340], DS126[341], DS126[342], DS126[343], DS126[354], DS126[355], DS126[356], DS126[358], DS126[362], DS126[363], DS126[364], DS126[365], DS126[366], DS126[367], DS126[369], DS126[370], DS126[371], DS126[372], DS126[373], DS126[374], DS126[378], DS126[379], DS126[380], DS126[381], DS126[382], DS126[383], DS126[384], DS126[385], DS126[386], DS126[387], DS126[388], DS126[389], DS126[390], DS126[391], DS126[392], DS126[393], DS126[394], DS126[395], DS126[396], DS126[397], DS126[398], DS126[399], DS126[400], DS126[401], DS126[402], DS126[403], DS126[404], DS126[405], DS126[406], DS126[407], DS126[408], DS126[409], DS126[410], DS126[411], DS126[412], DS126[413], DS126[414], DS126[415], DS126[416], DS126[417], DS126[418], DS126[419], DS126[420], DS126[421], DS126[422], DS126[423], DS126[424], DS126[425], DS126[426], DS126[427], DS126[428], DS126[429], DS126[430], DS126[431], DS126[432], DS126[433], DS126[434], DS126[435], DS126[440], DS126[441], DS126[442], DS126[443], DS126[444], DS126[445], DS126[446], DS126[447], DS126[450], DS126[451], DS126[452], DS126[453], DS126[454], DS126[455], DS126[456], DS126[457], DS126[458], DS126[461], DS126[462], DS126[463], DS126[464], DS126[465], DS126[466], DS126[467], DS126[468], DS126[469], DS126[470], DS126[471], DS126[472], DS126[473], DS126[474], DS126[475], DS126[476], DS126[477], DS126[478], DS126[479], DS126[480], DS126[481], DS126[482], DS126[483], DS126[484], DS126[485], DS126[486], DS126[487], DS126[489], DS126[490], DS126[491], DS126[492], DS126[493], DS126[494], DS126[495], DS126[496], DS126[499], DS126[500], DS126[503], DS126[506], DS126[507], DS126[508], DS126[509], DS126[510], DS126[511], DS126[512], DS126[513], DS126[514], DS126[515], DS126[516], DS126[517], DS126[518], DS126[519], DS126[520], DS126[521], DS126[522], DS126[523], DS126[524], DS126[525], DS126[526], DS126[527], DS126[528], DS126[529], DS126[530], DS126[531], DS126[532], DS126[533], DS126[534], DS126[535], DS126[536], DS126[537], DS126[538], DS126[539], DS126[540], DS126[541], DS126[542], DS126[543], DS126[544], DS126[545], DS126[546], DS126[547], DS126[548], DS126[549], DS126[550], DS126[551], DS126[552], DS126[553], DS126[554], DS126[555], DS126[556], DS126[557], DS126[558], DS126[559], DS126[560], DS126[561], DS126[562], DS126[563], DS126[564], DS126[565], DS126[566], DS126[567], DS126[568], DS126[569], DS126[570], DS126[571], DS126[572]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,126].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,126] is 6
### The list of all inequivalent reversible (64,28,12) DSs in group [64,126] is 
  
  
RDS126:=[ [ 2, 3, 4, 7, 8, 9, 13, 14, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 39, 44, 48, 49, 50, 53, 54, 55, 57, 58 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 19, 21, 27, 28, 29, 32, 39, 44, 46, 47, 48, 49, 50, 53, 54, 55, 57, 58 ], [ 2, 3, 4, 6, 7, 8, 11, 12, 13, 14, 19, 20, 21, 22, 28, 32, 39, 42, 44, 46, 47, 48, 49, 53, 54, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 14, 19, 25, 26, 27, 28, 29, 30, 31, 32, 39, 48, 49, 50, 53, 54, 55, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 14, 19, 27, 28, 29, 32, 39, 46, 47, 48, 49, 50, 53, 54, 55, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 19, 20, 22, 28, 32, 39, 42, 46, 47, 48, 49, 53, 54, 55, 57, 60, 64 ] ];
  
  
  
   
   
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