### 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 [64,117]. 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 [64,117].
    
    
# 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(64,117));' can be 
# used to create a list e of the elements of the group [64,117].
# In our list of (64,28,12) DSs in group [64,117], we have [1, 
# 2, 3, 4, 5, 9, 10, 11, 12, 13, 16, 22, 23, 25, 28, 
# 29, 31, 36, 40, 42, 43, 51, 52, 54, 56, 60, 61, 64].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[9], e[10], e[11], e[12], e[13], e[16], e[22], e[23], e[25], e[28], e[29], 
# e[31], e[36], e[40], e[42], e[43], e[51], e[52], e[54], e[56], e[60], e[61], e[64]]
# where e is the list of the elements of the group [64,117] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,117));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 117]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,117] is 1348
### The list of all inequivalent (64,28,12) DSs in group [64,117] is 
  
  
DS117:=[ [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 16, 22, 23, 25, 28, 29, 31, 36, 40, 42, 43, 51, 52, 54, 56, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 15, 16, 22, 23, 25, 29, 31, 38, 40, 42, 43, 49, 52, 54, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 22, 25, 29, 31, 36, 40, 42, 43, 49, 52, 54, 58, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 22, 25, 28, 29, 31, 36, 40, 42, 43, 44, 51, 52, 54, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 22, 23, 25, 29, 31, 36, 40, 42, 44, 45, 49, 52, 54, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 22, 23, 25, 28, 29, 31, 36, 40, 42, 45, 51, 52, 54, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 12, 13, 16, 18, 22, 23, 25, 31, 34, 35, 36, 40, 42, 43, 47, 55, 56, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 12, 13, 16, 18, 19, 22, 23, 25, 31, 34, 36, 41, 42, 43, 47, 54, 56, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 12, 13, 15, 16, 18, 22, 23, 26, 31, 38, 40, 42, 43, 46, 53, 54, 55, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 12, 13, 15, 16, 18, 22, 23, 25, 31, 35, 38, 40, 42, 43, 47, 53, 57, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 15, 16, 17, 18, 19, 22, 23, 29, 31, 34, 38, 40, 42, 43, 47, 49, 57, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 14, 15, 17, 18, 19, 22, 29, 31, 34, 36, 40, 42, 43, 47, 49, 57, 58, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 14, 15, 17, 18, 19, 22, 28, 29, 31, 34, 36, 40, 42, 43, 44, 47, 51, 57, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 14, 15, 17, 18, 19, 22, 23, 29, 31, 34, 36, 40, 42, 44, 45, 47, 49, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 14, 15, 17, 18, 19, 22, 23, 28, 29, 31, 34, 36, 40, 42, 45, 47, 51, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 16, 17, 18, 21, 30, 36, 39, 43, 46, 47, 48, 53, 54, 55, 56, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 16, 17, 18, 21, 25, 30, 34, 36, 39, 43, 47, 54, 56, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 16, 17, 18, 21, 23, 30, 36, 39, 44, 45, 46, 47, 48, 53, 54, 55, 56, 60 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 16, 17, 18, 21, 23, 25, 30, 34, 36, 39, 44, 45, 47, 54, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 17, 18, 21, 26, 30, 34, 35, 37, 39, 43, 44, 45, 46, 55, 56, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 17, 18, 21, 25, 26, 30, 35, 37, 39, 43, 44, 45, 48, 53, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 17, 18, 21, 23, 26, 30, 34, 35, 37, 39, 46, 55, 56, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 17, 18, 21, 23, 25, 26, 30, 35, 37, 39, 48, 53, 56, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 16, 17, 18, 21, 30, 38, 39, 43, 44, 46, 47, 48, 53, 54, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 16, 17, 18, 21, 25, 30, 34, 38, 39, 43, 44, 47, 54, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 16, 17, 18, 21, 23, 30, 38, 39, 45, 46, 47, 48, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 16, 17, 18, 21, 23, 25, 30, 34, 38, 39, 45, 47, 54, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 18, 21, 24, 28, 29, 31, 34, 36, 39, 48, 51, 52, 54, 56, 61, 63 ], [ 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, 7, 8, 9, 10, 11, 13, 19, 21, 25, 26, 28, 30, 33, 36, 37, 38, 39, 48, 50, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 18, 19, 21, 26, 28, 30, 33, 36, 37, 38, 41, 46, 50, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 21, 24, 28, 29, 30, 34, 36, 39, 40, 41, 48, 51, 54, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 18, 21, 24, 28, 29, 30, 36, 40, 48, 51, 53, 54, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 28, 29, 30, 36, 39, 46, 47, 48, 51, 53, 54, 55, 56 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 25, 28, 29, 30, 34, 36, 39, 47, 51, 54, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 19, 21, 25, 26, 30, 33, 37, 39, 48, 49, 50, 51, 55, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 19, 21, 24, 30, 34, 35, 37, 39, 48, 49, 50, 51, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 18, 19, 21, 26, 30, 33, 37, 41, 46, 49, 50, 51, 55, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 18, 19, 21, 24, 30, 35, 37, 41, 48, 49, 50, 51, 53, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 17, 18, 21, 26, 30, 34, 35, 37, 39, 46, 49, 50, 51, 55, 56, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 17, 18, 21, 25, 26, 30, 35, 37, 39, 48, 49, 50, 51, 53, 56, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 21, 29, 30, 33, 38, 39, 40, 41, 46, 47, 48, 49, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 21, 24, 29, 30, 34, 38, 39, 40, 41, 48, 49, 54, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 18, 21, 25, 29, 30, 33, 38, 40, 47, 49, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 18, 21, 24, 29, 30, 38, 40, 48, 49, 53, 54, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 21, 29, 30, 38, 39, 46, 47, 48, 49, 53, 54, 55, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 21, 25, 29, 30, 34, 38, 39, 47, 49, 54, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 19, 20, 23, 25, 30, 38, 41, 44, 46, 48, 49, 50, 51, 52, 56, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 19, 20, 23, 25, 28, 30, 38, 41, 46, 48, 50, 52, 56, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 18, 19, 20, 23, 28, 30, 33, 35, 36, 37, 38, 41, 43, 44, 50, 52, 54, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 15, 18, 19, 20, 23, 30, 33, 35, 37, 41, 43, 44, 49, 50, 51, 52, 54, 56, 58 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 15, 16, 20, 23, 27, 29, 30, 34, 38, 39, 40, 41, 43, 44, 50, 52, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 19, 20, 23, 30, 33, 35, 38, 41, 44, 49, 50, 51, 52, 54, 56, 59, 64 ], [ 1, 2, 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32, 33, 39, 40, 45, 47, 52, 55, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 22, 26, 28, 33, 34, 39, 40, 42, 47, 53, 55, 56, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 20, 22, 23, 26, 35, 36, 39, 40, 47, 51, 53, 55, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 27, 32, 33, 37, 41, 44, 50, 52, 55, 56, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 25, 27, 28, 33, 37, 41, 46, 49, 50, 55, 56, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 21, 29, 33, 38, 39, 42, 51, 53, 55, 56, 58, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 20, 25, 28, 33, 37, 39, 41, 42, 55, 56, 57, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 20, 25, 28, 33, 34, 37, 39, 42, 51, 53, 55, 56, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 20, 25, 28, 29, 33, 35, 37, 39, 42, 50, 54, 55, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 20, 22, 27, 33, 35, 36, 37, 41, 44, 49, 50, 54, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 19, 20, 23, 25, 28, 33, 37, 39, 40, 42, 43, 55, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 25, 28, 33, 37, 39, 40, 41, 46, 55, 56, 57, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 23, 28, 32, 35, 37, 39, 40, 52, 53, 55, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 23, 26, 27, 28, 35, 36, 41, 47, 49, 50, 53, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 23, 26, 27, 28, 30, 33, 35, 41, 47, 50, 52, 53, 54, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 22, 23, 27, 35, 36, 41, 42, 50, 53, 55, 56, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 23, 26, 30, 35, 39, 40, 43, 47, 52, 55, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 23, 26, 28, 35, 36, 39, 40, 41, 47, 53, 56, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 29, 30, 33, 37, 41, 44, 50, 52, 53, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 21, 28, 29, 33, 36, 39, 42, 49, 53, 55, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 22, 23, 27, 33, 35, 37, 41, 42, 50, 54, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 23, 25, 26, 30, 31, 33, 39, 40, 45, 56, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 26, 31, 33, 34, 36, 38, 41, 43, 52, 56, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 24, 29, 31, 33, 34, 45, 46, 49, 50, 52, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 24, 25, 29, 31, 33, 34, 43, 48, 49, 50, 52, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 23, 25, 30, 31, 33, 39, 41, 43, 47, 48, 56, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 23, 25, 26, 30, 31, 33, 40, 41, 43, 56, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 21, 23, 28, 33, 38, 39, 42, 43, 50, 51, 54, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 21, 23, 28, 29, 33, 37, 38, 39, 42, 43, 49, 54, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 21, 34, 35, 36, 39, 42, 45, 49, 50, 54, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 21, 28, 33, 36, 39, 42, 45, 50, 51, 54, 59, 61, 63 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 728
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS117[2], DS117[9], DS117[15], DS117[21], DS117[27], DS117[34], DS117[51], DS117[55], DS117[61], DS117[69], DS117[70], DS117[71], DS117[77], DS117[81], DS117[87], DS117[91], DS117[92], DS117[93], DS117[94], DS117[105], DS117[106], DS117[107], DS117[109], DS117[111], DS117[112], DS117[114], DS117[115], DS117[122], DS117[127], DS117[128], DS117[129], DS117[132], DS117[137], DS117[140], DS117[141], DS117[144], DS117[147], DS117[148], DS117[149], DS117[155], DS117[156], DS117[158], DS117[164], DS117[166], DS117[167], DS117[170], DS117[171], DS117[172], DS117[173], DS117[178], DS117[194], DS117[196], DS117[197], DS117[198], DS117[200], DS117[201], DS117[202], DS117[203], DS117[205], DS117[209], DS117[226], DS117[227], DS117[234], DS117[241], DS117[245], DS117[247], DS117[248], DS117[250], DS117[254], DS117[255], DS117[273], DS117[276], DS117[277], DS117[280], DS117[281], DS117[283], DS117[285], DS117[293], DS117[294], DS117[305], DS117[312], DS117[313], DS117[314], DS117[323], DS117[328], DS117[331], DS117[334], DS117[339], DS117[346], DS117[350], DS117[355], DS117[356], DS117[357], DS117[358], DS117[361], DS117[362], DS117[366], DS117[373], DS117[378], DS117[379], DS117[381], DS117[391], DS117[393], DS117[394], DS117[401], DS117[402], DS117[405], DS117[411], DS117[412], DS117[413], DS117[417], DS117[419], DS117[420], DS117[424], DS117[429], DS117[431], DS117[433], DS117[442], DS117[443], DS117[446], DS117[448], DS117[452], DS117[453], DS117[455], DS117[458], DS117[460], DS117[462], DS117[464], DS117[465], DS117[467], DS117[469], DS117[472], DS117[477], DS117[478], DS117[483], DS117[484], DS117[487], DS117[488], DS117[489], DS117[490], DS117[495], DS117[500], DS117[501], DS117[512], DS117[522], DS117[526], DS117[527], DS117[529], DS117[530], DS117[531], DS117[532], DS117[533], DS117[534], DS117[535], DS117[538], DS117[539], DS117[540], DS117[547], DS117[550], DS117[553], DS117[554], DS117[557], DS117[558], DS117[564], DS117[565], DS117[573], DS117[574], DS117[579], DS117[583], DS117[586], DS117[587], DS117[588], DS117[589], DS117[592], DS117[593], DS117[594], DS117[595], DS117[596], DS117[599], DS117[600], DS117[601], DS117[602], DS117[603], DS117[604], DS117[605], DS117[606], DS117[607], DS117[608], DS117[609], DS117[611], DS117[613], DS117[614], DS117[615], DS117[616], DS117[618], DS117[619], DS117[620], DS117[622], DS117[623], DS117[624], DS117[625], DS117[626], DS117[628], DS117[629], DS117[631], DS117[632], DS117[636], DS117[637], DS117[638], DS117[639], DS117[643], DS117[646], DS117[655], DS117[656], DS117[657], DS117[663], DS117[666], DS117[667], DS117[668], DS117[670], DS117[671], DS117[672], DS117[673], DS117[674], DS117[675], DS117[676], DS117[679], DS117[681], DS117[682], DS117[685], DS117[686], DS117[687], DS117[688], DS117[689], DS117[690], DS117[692], DS117[693], DS117[695], DS117[696], DS117[697], DS117[698], DS117[700], DS117[701], DS117[709], DS117[710], DS117[715], DS117[716], DS117[718], DS117[719], DS117[720], DS117[721], DS117[722], DS117[725], DS117[726], DS117[739], DS117[740], DS117[741], DS117[744], DS117[745], DS117[746], DS117[747], DS117[750], DS117[753], DS117[754], DS117[756], DS117[757], DS117[764], DS117[765], DS117[766], DS117[767], DS117[771], DS117[775], DS117[777], DS117[780], DS117[781], DS117[782], DS117[783], DS117[785], DS117[786], DS117[789], DS117[790], DS117[791], DS117[792], DS117[793], DS117[795], DS117[796], DS117[797], DS117[798], DS117[799], DS117[800], DS117[801], DS117[802], DS117[804], DS117[805], DS117[806], DS117[807], DS117[809], DS117[810], DS117[811], DS117[813], DS117[814], DS117[815], DS117[816], DS117[817], DS117[818], DS117[819], DS117[820], DS117[821], DS117[823], DS117[824], DS117[825], DS117[826], DS117[827], DS117[828], DS117[829], DS117[830], DS117[831], DS117[832], DS117[833], DS117[834], DS117[835], DS117[836], DS117[837], DS117[838], DS117[839], DS117[841], DS117[842], DS117[843], DS117[844], DS117[845], DS117[846], DS117[847], DS117[848], DS117[849], DS117[850], DS117[851], DS117[852], DS117[853], DS117[854], DS117[855], DS117[856], DS117[858], DS117[859], DS117[860], DS117[861], DS117[862], DS117[863], DS117[864], DS117[865], DS117[866], DS117[867], DS117[868], DS117[869], DS117[870], DS117[872], DS117[873], DS117[874], DS117[875], DS117[876], DS117[877], DS117[878], DS117[879], DS117[880], DS117[881], DS117[882], DS117[883], DS117[884], DS117[885], DS117[886], DS117[887], DS117[888], DS117[889], DS117[890], DS117[891], DS117[892], DS117[893], DS117[894], DS117[895], DS117[898], DS117[899], DS117[903], DS117[904], DS117[905], DS117[906], DS117[907], DS117[908], DS117[909], DS117[910], DS117[911], DS117[912], DS117[923], DS117[930], DS117[931], DS117[932], DS117[933], DS117[934], DS117[935], DS117[936], DS117[938], DS117[939], DS117[940], DS117[941], DS117[942], DS117[943], DS117[944], DS117[945], DS117[948], DS117[951], DS117[953], DS117[954], DS117[955], DS117[956], DS117[958], DS117[959], DS117[960], DS117[961], DS117[962], DS117[963], DS117[964], DS117[965], DS117[966], DS117[967], DS117[968], DS117[969], DS117[970], DS117[971], DS117[972], DS117[973], DS117[974], DS117[975], DS117[976], DS117[977], DS117[979], DS117[980], DS117[981], DS117[983], DS117[984], DS117[986], DS117[987], DS117[991], DS117[993], DS117[994], DS117[996], DS117[997], DS117[998], DS117[999], DS117[1000], DS117[1001], DS117[1002], DS117[1003], DS117[1004], DS117[1005], DS117[1007], DS117[1008], DS117[1009], DS117[1011], DS117[1013], DS117[1015], DS117[1018], DS117[1019], DS117[1020], DS117[1021], DS117[1024], DS117[1025], DS117[1026], DS117[1027], DS117[1028], DS117[1029], DS117[1030], DS117[1031], DS117[1033], DS117[1034], DS117[1036], DS117[1038], DS117[1039], DS117[1041], DS117[1042], DS117[1044], DS117[1045], DS117[1046], DS117[1047], DS117[1048], DS117[1049], DS117[1050], DS117[1061], DS117[1064], DS117[1065], DS117[1066], DS117[1067], DS117[1068], DS117[1069], DS117[1070], DS117[1071], DS117[1072], DS117[1073], DS117[1074], DS117[1075], DS117[1080], DS117[1081], DS117[1083], DS117[1084], DS117[1085], DS117[1086], DS117[1087], DS117[1088], DS117[1089], DS117[1090], DS117[1091], DS117[1093], DS117[1094], DS117[1095], DS117[1096], DS117[1097], DS117[1099], DS117[1100], DS117[1101], DS117[1102], DS117[1103], DS117[1104], DS117[1105], DS117[1106], DS117[1107], DS117[1108], DS117[1109], DS117[1110], DS117[1111], DS117[1112], DS117[1113], DS117[1114], DS117[1115], DS117[1116], DS117[1117], DS117[1118], DS117[1119], DS117[1120], DS117[1121], DS117[1122], DS117[1123], DS117[1124], DS117[1125], DS117[1126], DS117[1127], DS117[1131], DS117[1132], DS117[1134], DS117[1135], DS117[1136], DS117[1137], DS117[1138], DS117[1139], DS117[1140], DS117[1141], DS117[1142], DS117[1143], DS117[1144], DS117[1145], DS117[1146], DS117[1148], DS117[1151], DS117[1152], DS117[1153], DS117[1156], DS117[1157], DS117[1158], DS117[1159], DS117[1160], DS117[1161], DS117[1162], DS117[1163], DS117[1164], DS117[1165], DS117[1166], DS117[1167], DS117[1168], DS117[1169], DS117[1170], DS117[1171], DS117[1172], DS117[1173], DS117[1174], DS117[1175], DS117[1176], DS117[1177], DS117[1178], DS117[1180], DS117[1181], DS117[1182], DS117[1183], DS117[1184], DS117[1185], DS117[1186], DS117[1188], DS117[1189], DS117[1192], DS117[1193], DS117[1194], DS117[1195], DS117[1196], DS117[1197], DS117[1198], DS117[1199], DS117[1200], DS117[1201], DS117[1202], DS117[1203], DS117[1204], DS117[1205], DS117[1206], DS117[1207], DS117[1208], DS117[1209], DS117[1210], DS117[1211], DS117[1212], DS117[1213], DS117[1214], DS117[1215], DS117[1216], DS117[1217], DS117[1218], DS117[1219], DS117[1220], DS117[1221], DS117[1222], DS117[1223], DS117[1224], DS117[1225], DS117[1226], DS117[1227], DS117[1228], DS117[1229], DS117[1230], DS117[1231], DS117[1232], DS117[1233], DS117[1234], DS117[1235], DS117[1236], DS117[1237], DS117[1238], DS117[1239], DS117[1240], DS117[1241], DS117[1242], DS117[1244], DS117[1246], DS117[1247], DS117[1248], DS117[1249], DS117[1250], DS117[1251], DS117[1252], DS117[1253], DS117[1254], DS117[1257], DS117[1259], DS117[1263], DS117[1268], DS117[1271], DS117[1272], DS117[1273], DS117[1274], DS117[1275], DS117[1276], DS117[1277], DS117[1279], DS117[1280], DS117[1281], DS117[1282], DS117[1283], DS117[1284], DS117[1285], DS117[1292], DS117[1293], DS117[1294], DS117[1295], DS117[1296], DS117[1297], DS117[1299], DS117[1300], DS117[1301], DS117[1302], DS117[1303], DS117[1304], DS117[1305], DS117[1306], DS117[1307], DS117[1308], DS117[1309], DS117[1310], DS117[1311], DS117[1312], DS117[1313], DS117[1314], DS117[1315], DS117[1316], DS117[1317], DS117[1318], DS117[1319], DS117[1320], DS117[1321], DS117[1322], DS117[1323], DS117[1324], DS117[1325], DS117[1326], DS117[1327], DS117[1328], DS117[1329], DS117[1330], DS117[1331], DS117[1332], DS117[1333], DS117[1334], DS117[1335], DS117[1336], DS117[1337], DS117[1338], DS117[1339], DS117[1340], DS117[1341], DS117[1342], DS117[1343], DS117[1344], DS117[1345], DS117[1346], DS117[1347], DS117[1348]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,117].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,117] is 86
### The list of all inequivalent reversible (64,28,12) DSs in group [64,117] is 
  
  
RDS117:=[ [ 2, 3, 4, 8, 9, 10, 16, 17, 25, 28, 29, 32, 33, 35, 36, 41, 44, 47, 51, 52, 53, 55, 56, 57, 58, 60, 61, 64 ], [ 2, 3, 4, 8, 9, 10, 16, 17, 23, 25, 28, 29, 32, 33, 35, 36, 41, 43, 45, 47, 51, 52, 53, 55, 56, 57, 59, 61 ], [ 2, 3, 4, 8, 9, 10, 15, 16, 17, 25, 29, 32, 33, 35, 38, 41, 44, 47, 49, 52, 53, 55, 57, 58, 60, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 10, 15, 16, 17, 23, 25, 29, 32, 33, 35, 38, 41, 43, 45, 47, 49, 52, 53, 55, 57, 59, 61, 62 ], [ 2, 3, 4, 8, 9, 10, 13, 16, 17, 25, 28, 29, 32, 34, 36, 41, 44, 47, 51, 52, 54, 56, 57, 58, 60, 61, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 13, 16, 17, 23, 25, 28, 29, 32, 34, 36, 41, 43, 45, 47, 51, 52, 54, 56, 57, 59, 61, 63 ], [ 2, 3, 4, 8, 9, 10, 13, 15, 16, 17, 25, 29, 32, 34, 38, 41, 44, 47, 49, 52, 54, 57, 58, 60, 61, 62, 63, 64 ], [ 2, 3, 4, 8, 9, 10, 13, 15, 16, 17, 23, 25, 29, 32, 34, 38, 41, 43, 45, 47, 49, 52, 54, 57, 59, 61, 62, 63 ], [ 2, 3, 4, 6, 8, 9, 10, 16, 17, 20, 22, 25, 28, 29, 32, 33, 35, 36, 41, 42, 47, 51, 52, 53, 55, 56, 57, 61 ], [ 2, 3, 4, 6, 8, 9, 10, 15, 16, 17, 20, 22, 25, 29, 32, 33, 35, 38, 41, 42, 47, 49, 52, 53, 55, 57, 61, 62 ], [ 2, 3, 4, 6, 8, 9, 10, 13, 16, 17, 20, 22, 25, 28, 29, 32, 34, 36, 41, 42, 47, 51, 52, 54, 56, 57, 61, 63 ], [ 2, 3, 4, 6, 8, 9, 10, 13, 15, 16, 17, 20, 22, 25, 29, 32, 34, 38, 41, 42, 47, 49, 52, 54, 57, 61, 62, 63 ], [ 2, 3, 4, 5, 8, 16, 17, 20, 21, 25, 30, 31, 32, 35, 36, 41, 42, 44, 47, 54, 55, 56, 57, 58, 60, 61, 63, 64 ], [ 2, 3, 4, 5, 8, 16, 17, 20, 21, 25, 28, 30, 31, 32, 35, 36, 41, 42, 47, 49, 51, 54, 55, 56, 57, 61, 62, 63 ], [ 2, 3, 4, 5, 8, 16, 17, 20, 21, 23, 25, 30, 31, 32, 35, 36, 41, 42, 43, 45, 47, 54, 55, 56, 57, 59, 61, 63 ], [ 2, 3, 4, 5, 8, 13, 16, 17, 20, 21, 25, 30, 31, 32, 33, 34, 36, 41, 42, 44, 47, 53, 56, 57, 58, 60, 61, 64 ], [ 2, 3, 4, 5, 8, 13, 16, 17, 20, 21, 25, 28, 30, 31, 32, 33, 34, 36, 41, 42, 47, 49, 51, 53, 56, 57, 61, 62 ], [ 2, 3, 4, 5, 8, 13, 16, 17, 20, 21, 23, 25, 30, 31, 32, 33, 34, 36, 41, 42, 43, 45, 47, 53, 56, 57, 59, 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