### 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 [64,13]. 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 [64,13]. # 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(64,13));' can be # used to create a list e of the elements of the group [64,13]. # In our list of (64,28,12) DSs in group [64,13], we have [1, # 2, 3, 4, 5, 8, 9, 11, 12, 15, 22, 26, 28, 31, 32, # 39, 40, 41, 42, 44, 46, 52, 54, 58, 60, 61, 63, 64]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[8], e[9], e[11], e[12], e[15], e[22], e[26], e[28], e[31], e[32], e[39], # e[40], e[41], e[42], e[44], e[46], e[52], e[54], e[58], e[60], e[61], e[63], e[64]] # where e is the list of the elements of the group [64,13] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,13));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 13] ### The number of inequivalent (64,28,12) DSs in group [64,13] is 688 ### The list of all inequivalent (64,28,12) DSs in group [64,13] is DS13:=[ [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 15, 22, 26, 28, 31, 32, 39, 40, 41, 42, 44, 46, 52, 54, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 15, 22, 23, 26, 28, 31, 32, 39, 40, 41, 42, 43, 45, 46, 52, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 16, 22, 25, 28, 31, 32, 33, 34, 37, 39, 40, 41, 42, 52, 54, 55, 59, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 14, 16, 22, 25, 28, 31, 32, 35, 37, 39, 40, 41, 42, 52, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 19, 21, 23, 34, 37, 38, 39, 43, 46, 47, 48, 50, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 19, 21, 23, 24, 34, 37, 38, 39, 48, 50, 56, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 14, 19, 21, 23, 25, 38, 39, 43, 44, 45, 50, 53, 54, 55, 56, 57, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 11, 13, 14, 19, 21, 23, 25, 26, 38, 39, 44, 47, 48, 50, 53, 54, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 19, 21, 23, 27, 28, 29, 39, 43, 46, 47, 48, 49, 51, 54, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 19, 21, 23, 24, 27, 28, 29, 39, 48, 49, 51, 54, 57, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 16, 17, 21, 25, 27, 28, 29, 33, 34, 35, 37, 41, 49, 51, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 21, 25, 27, 28, 29, 36, 41, 49, 51, 53, 54, 55, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 21, 25, 27, 28, 29, 35, 38, 39, 40, 41, 49, 51, 53, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 21, 25, 27, 28, 29, 33, 35, 38, 39, 40, 41, 49, 51, 54, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 19, 21, 25, 27, 28, 29, 38, 39, 49, 51, 53, 54, 55, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 16, 21, 25, 27, 28, 29, 33, 37, 39, 40, 41, 49, 51, 55, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 16, 17, 21, 25, 27, 28, 29, 37, 41, 49, 51, 53, 54, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 25, 28, 31, 32, 33, 34, 36, 38, 39, 41, 42, 52, 55, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 19, 25, 28, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 52, 54, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 17, 25, 28, 31, 32, 34, 36, 38, 40, 41, 42, 52, 53, 54, 55, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 25, 28, 31, 32, 34, 35, 36, 37, 39, 41, 42, 52, 53, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 19, 25, 28, 31, 32, 34, 36, 37, 39, 40, 42, 52, 53, 54, 55, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 17, 25, 28, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 52, 54, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 17, 19, 25, 28, 31, 32, 33, 34, 36, 37, 42, 52, 55, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 19, 21, 23, 28, 31, 32, 39, 43, 46, 47, 48, 52, 54, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 19, 21, 23, 24, 28, 31, 32, 39, 48, 52, 54, 57, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 25, 28, 31, 32, 34, 37, 38, 39, 41, 42, 52, 53, 54, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 21, 25, 28, 31, 32, 34, 38, 39, 40, 41, 52, 53, 55, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 19, 25, 28, 31, 32, 34, 35, 37, 38, 39, 40, 42, 52, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 17, 25, 28, 31, 32, 33, 34, 37, 38, 40, 41, 42, 52, 55, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 17, 19, 25, 28, 31, 32, 34, 35, 37, 38, 42, 52, 53, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 16, 25, 28, 31, 32, 33, 34, 35, 39, 41, 42, 52, 54, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 16, 19, 25, 28, 31, 32, 34, 39, 40, 42, 52, 53, 54, 55, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 16, 19, 25, 28, 31, 32, 33, 34, 39, 40, 42, 52, 55, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 16, 17, 25, 28, 31, 32, 34, 35, 40, 41, 42, 52, 53, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 16, 17, 19, 25, 28, 31, 32, 34, 42, 52, 53, 54, 55, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 16, 17, 19, 25, 28, 31, 32, 33, 34, 42, 52, 55, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 25, 28, 31, 32, 35, 36, 38, 39, 41, 42, 52, 53, 54, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 25, 28, 31, 32, 33, 35, 36, 38, 39, 41, 42, 52, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 17, 25, 28, 31, 32, 35, 36, 38, 40, 41, 42, 52, 53, 54, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 17, 25, 28, 31, 32, 33, 35, 36, 38, 40, 41, 42, 52, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 17, 21, 25, 28, 31, 32, 33, 35, 36, 37, 38, 41, 52, 54, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 17, 19, 25, 28, 31, 32, 33, 36, 38, 42, 52, 54, 55, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 25, 28, 31, 32, 36, 37, 39, 41, 42, 52, 53, 55, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 25, 28, 31, 32, 33, 36, 37, 39, 41, 42, 52, 54, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 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63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 43, 44, 47, 48, 50, 51, 52, 53, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 33, 44, 47, 48, 50, 51, 52, 54, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 33, 43, 44, 47, 48, 50, 51, 52, 54, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 27, 28, 30, 43, 46, 47, 48, 49, 53, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 27, 28, 30, 33, 43, 46, 47, 48, 49, 54, 60, 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, 33, 43, 46, 47, 50, 51, 52, 54, 58, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 25, 27, 46, 47, 49, 51, 52, 53, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 25, 27, 33, 46, 47, 49, 51, 52, 54, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 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27, 33, 49, 51, 52, 54, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 22, 26, 29, 31, 34, 37, 38, 41, 42, 50, 53, 54, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 22, 26, 29, 31, 34, 37, 38, 41, 42, 43, 50, 53, 54, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 22, 26, 29, 31, 33, 34, 37, 38, 41, 42, 50, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 22, 26, 29, 31, 33, 34, 37, 38, 41, 42, 43, 50, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 20, 22, 26, 27, 29, 31, 33, 36, 37, 38, 49, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 20, 22, 26, 27, 29, 31, 33, 36, 37, 38, 43, 49, 55, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 34, 37, 48, 50, 51, 52, 53, 56, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 34, 37, 43, 48, 50, 51, 52, 53, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 33, 34, 37, 48, 50, 51, 52, 54, 56, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 33, 34, 37, 43, 48, 50, 51, 52, 54, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 20, 22, 27, 33, 35, 36, 48, 49, 51, 52, 54, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 20, 22, 27, 33, 35, 36, 43, 48, 49, 51, 52, 54, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 22, 26, 29, 31, 33, 36, 37, 41, 42, 50, 53, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 22, 26, 29, 31, 33, 36, 37, 41, 42, 43, 50, 53, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 22, 26, 27, 29, 31, 36, 37, 41, 42, 49, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 22, 26, 27, 29, 31, 36, 37, 41, 42, 43, 49, 54, 55, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 21, 22, 33, 35, 36, 48, 50, 51, 52, 53, 56, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 21, 22, 33, 35, 36, 43, 48, 50, 51, 52, 53, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 21, 22, 27, 35, 36, 48, 49, 51, 52, 54, 56, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 21, 22, 27, 35, 36, 43, 48, 49, 51, 52, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 22, 26, 27, 29, 31, 34, 36, 38, 41, 42, 49, 53, 54, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 22, 26, 27, 29, 31, 34, 36, 38, 41, 42, 43, 49, 53, 54, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 22, 26, 27, 29, 31, 33, 34, 36, 38, 41, 42, 49, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 22, 26, 27, 29, 31, 33, 34, 36, 38, 41, 42, 43, 49, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 20, 22, 26, 27, 29, 31, 38, 49, 53, 54, 55, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 20, 22, 26, 27, 29, 31, 38, 43, 49, 53, 54, 55, 56, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 27, 34, 36, 48, 49, 51, 52, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 27, 34, 36, 43, 48, 49, 51, 52, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 27, 33, 34, 36, 48, 49, 51, 52, 54, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 27, 33, 34, 36, 43, 48, 49, 51, 52, 54, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 22, 27, 35, 37, 48, 49, 51, 52, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 22, 27, 35, 37, 43, 48, 49, 51, 52, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 22, 26, 29, 31, 33, 41, 42, 50, 53, 55, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 22, 26, 29, 31, 33, 41, 42, 43, 50, 53, 55, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 22, 26, 27, 29, 31, 41, 42, 49, 54, 55, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 22, 26, 27, 29, 31, 41, 42, 43, 49, 54, 55, 56, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 33, 35, 37, 48, 50, 51, 52, 53, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 33, 35, 37, 43, 48, 50, 51, 52, 53, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 27, 35, 37, 48, 49, 51, 52, 54, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 27, 35, 37, 43, 48, 49, 51, 52, 54, 63, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 209 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS13[6], DS13[10], DS13[11], DS13[13], DS13[27], DS13[37], DS13[38], DS13[44], DS13[46], DS13[54], DS13[56], DS13[60], DS13[62], DS13[65], DS13[68], DS13[75], DS13[77], DS13[87], DS13[93], DS13[94], DS13[96], DS13[99], DS13[101], DS13[105], DS13[117], DS13[118], DS13[125], DS13[147], DS13[149], DS13[150], DS13[157], DS13[161], DS13[170], DS13[175], DS13[177], DS13[179], DS13[189], DS13[205], DS13[207], DS13[208], DS13[209], DS13[210], DS13[211], DS13[212], DS13[220], DS13[225], DS13[226], DS13[227], DS13[233], DS13[240], DS13[244], DS13[246], DS13[250], DS13[252], DS13[260], DS13[263], DS13[264], DS13[271], DS13[276], DS13[278], DS13[279], DS13[280], DS13[282], DS13[283], DS13[286], DS13[289], DS13[290], DS13[294], DS13[297], DS13[309], DS13[316], DS13[323], DS13[328], DS13[340], DS13[342], DS13[343], DS13[344], DS13[350], DS13[367], DS13[377], DS13[384], DS13[385], DS13[388], DS13[390], DS13[392], DS13[394], DS13[398], DS13[402], DS13[408], DS13[409], DS13[411], DS13[415], DS13[418], DS13[419], DS13[420], DS13[421], DS13[422], DS13[423], DS13[424], DS13[425], DS13[426], DS13[427], DS13[428], DS13[429], DS13[430], DS13[431], DS13[432], DS13[433], DS13[434], DS13[439], DS13[440], DS13[441], DS13[442], DS13[443], DS13[444], DS13[445], DS13[446], DS13[447], DS13[448], DS13[449], DS13[450], DS13[451], DS13[452], DS13[453], DS13[454], DS13[459], DS13[464], DS13[465], DS13[466], DS13[467], DS13[478], DS13[486], DS13[497], DS13[498], DS13[502], DS13[508], DS13[511], DS13[512], DS13[514], DS13[518], DS13[525], DS13[526], DS13[528], DS13[529], DS13[531], DS13[539], DS13[542], DS13[544], DS13[545], DS13[553], DS13[555], DS13[556], DS13[561], DS13[564], DS13[565], DS13[567], DS13[568], DS13[572], DS13[576], DS13[584], DS13[587], DS13[591], DS13[601], DS13[602], DS13[603], DS13[605], DS13[607], DS13[610], DS13[617], DS13[619], DS13[620], DS13[629], DS13[637], DS13[638], DS13[648], DS13[649], DS13[650], DS13[651], DS13[652], DS13[655], DS13[656], DS13[657], DS13[658], DS13[661], DS13[662], DS13[663], DS13[664], DS13[665], DS13[666], DS13[667], DS13[668], DS13[669], DS13[670], DS13[671], DS13[672], DS13[673], DS13[674], DS13[675], DS13[676], DS13[677], DS13[678], DS13[681], DS13[682], DS13[683], DS13[684], DS13[685], DS13[686], DS13[687], DS13[688]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,13]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,13] is 8 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,13] is RDS13:=[ [ 2, 3, 5, 6, 7, 8, 10, 13, 14, 15, 17, 24, 26, 32, 33, 34, 36, 39, 40, 42, 43, 44, 47, 52, 53, 57, 59, 60 ], [ 2, 3, 5, 6, 7, 8, 10, 13, 14, 15, 17, 23, 26, 32, 33, 34, 36, 39, 40, 42, 43, 45, 46, 52, 53, 57, 59, 61 ], [ 2, 3, 4, 5, 6, 7, 8, 10, 13, 14, 15, 18, 19, 24, 26, 32, 33, 34, 36, 41, 42, 43, 44, 47, 52, 53, 59, 60 ], [ 2, 3, 4, 5, 6, 7, 8, 10, 13, 14, 15, 18, 19, 23, 26, 32, 33, 34, 36, 41, 42, 43, 45, 46, 52, 53, 59, 61 ], [ 1, 2, 3, 8, 10, 13, 14, 15, 17, 20, 21, 22, 24, 26, 32, 33, 34, 36, 39, 40, 43, 44, 47, 52, 53, 57, 59, 60 ], [ 1, 2, 3, 8, 10, 13, 14, 15, 17, 20, 21, 22, 23, 26, 32, 33, 34, 36, 39, 40, 43, 45, 46, 52, 53, 57, 59, 61 ], [ 1, 2, 3, 4, 8, 10, 13, 14, 15, 18, 19, 20, 21, 22, 24, 26, 32, 33, 34, 36, 41, 43, 44, 47, 52, 53, 59, 60 ], [ 1, 2, 3, 4, 8, 10, 13, 14, 15, 18, 19, 20, 21, 22, 23, 26, 32, 33, 34, 36, 41, 43, 45, 46, 52, 53, 59, 61 ] ]; ########################### 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