### 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 [64,118]. 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 [64,118]. # 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(64,118));' can be # used to create a list e of the elements of the group [64,118]. # In our list of (64,28,12) DSs in group [64,118], we have [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]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[6], e[9], e[10], e[12], e[13], e[14], e[18], e[20], e[24], e[29], e[31], # e[33], e[38], e[40], e[46], e[47], e[49], e[55], e[56], e[57], e[61], e[62], e[63]] # where e is the list of the elements of the group [64,118] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,118));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 118] ### The number of inequivalent (64,28,12) DSs in group [64,118] is 320 ### The list of all inequivalent (64,28,12) DSs in group [64,118] is DS118:=[ [ 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, 23, 29, 31, 33, 38, 40, 44, 45, 49, 55, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 20, 23, 24, 30, 33, 35, 38, 40, 44, 45, 48, 52, 54, 56, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 18, 20, 23, 24, 26, 30, 33, 38, 40, 44, 45, 47, 52, 55, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 20, 23, 26, 31, 33, 38, 40, 44, 45, 46, 55, 56, 57, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 18, 20, 23, 24, 31, 35, 38, 40, 44, 45, 48, 53, 56, 57, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 26, 27, 29, 30, 31, 32, 35, 42, 43, 44, 45, 46, 50, 55, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 24, 26, 29, 30, 31, 32, 35, 42, 43, 44, 45, 47, 49, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 23, 26, 30, 31, 32, 35, 42, 43, 45, 46, 49, 50, 51, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 23, 26, 27, 29, 30, 31, 32, 35, 42, 46, 50, 55, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 23, 26, 27, 29, 30, 31, 32, 35, 42, 43, 46, 50, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 23, 24, 26, 30, 31, 32, 35, 42, 45, 47, 49, 50, 51, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 23, 24, 26, 29, 30, 31, 32, 35, 42, 47, 49, 55, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 15, 18, 20, 21, 23, 24, 26, 29, 30, 31, 32, 35, 42, 43, 47, 49, 55, 60, 62, 64 ], [ 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, 27, 29, 30, 31, 32, 38, 40, 43, 46, 50, 57, 60, 61, 64 ], [ 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, 15, 16, 18, 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55, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 17, 18, 21, 23, 29, 30, 38, 40, 43, 48, 50, 55, 58, 59, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 17, 18, 21, 23, 29, 30, 33, 38, 40, 48, 50, 53, 54, 55, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 17, 18, 21, 23, 24, 29, 30, 38, 40, 46, 47, 48, 50, 55, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 17, 18, 21, 23, 24, 29, 30, 31, 38, 40, 46, 48, 52, 55, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 20, 24, 31, 34, 35, 36, 40, 48, 49, 50, 51, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 20, 24, 27, 31, 34, 35, 36, 40, 48, 51, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 31, 35, 38, 40, 48, 49, 50, 51, 53, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 27, 31, 35, 38, 40, 48, 51, 53, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 26, 29, 30, 36, 37, 38, 39, 40, 42, 44, 50, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 26, 29, 30, 31, 36, 38, 39, 40, 42, 44, 52, 54, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 26, 28, 29, 31, 36, 38, 39, 40, 42, 46, 51, 54, 55, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 25, 29, 31, 36, 37, 38, 39, 40, 42, 45, 49, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 25, 26, 29, 31, 36, 38, 39, 40, 42, 48, 49, 54, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 23, 30, 35, 36, 37, 38, 39, 40, 45, 48, 50, 51, 56, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 23, 30, 31, 35, 36, 38, 39, 40, 45, 48, 51, 52, 54, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 29, 31, 34, 35, 38, 40, 46, 47, 48, 49, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 29, 30, 31, 33, 38, 40, 44, 52, 55, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 28, 29, 31, 33, 38, 40, 46, 51, 55, 56, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 25, 26, 29, 31, 33, 38, 40, 48, 49, 55, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 24, 29, 31, 34, 35, 38, 40, 48, 49, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 24, 28, 29, 31, 35, 38, 40, 48, 51, 53, 56, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 23, 29, 31, 36, 37, 38, 40, 48, 49, 55, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 26, 29, 30, 33, 38, 42, 44, 50, 55, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 25, 29, 31, 33, 38, 42, 45, 49, 55, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 23, 29, 31, 36, 38, 42, 48, 49, 54, 55, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 29, 30, 34, 35, 38, 40, 46, 47, 48, 50, 55, 56, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 25, 29, 30, 31, 33, 38, 40, 45, 52, 55, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 25, 26, 29, 30, 33, 38, 40, 48, 50, 55, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 24, 29, 30, 34, 35, 38, 40, 48, 50, 55, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 23, 29, 30, 36, 37, 38, 40, 48, 50, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 23, 29, 30, 31, 36, 38, 40, 48, 52, 54, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 19, 21, 22, 23, 25, 30, 31, 32, 43, 44, 47, 49, 50, 51, 53, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 19, 21, 22, 23, 24, 25, 30, 31, 32, 44, 46, 49, 50, 51, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 16, 22, 23, 26, 27, 28, 31, 41, 42, 46, 47, 49, 52, 53, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 16, 22, 23, 24, 27, 28, 31, 33, 41, 42, 43, 45, 47, 48, 49, 52, 54, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 16, 19, 21, 22, 23, 27, 28, 31, 46, 47, 48, 49, 52, 53, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 16, 19, 21, 22, 23, 24, 27, 28, 31, 43, 48, 49, 52, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 19, 21, 22, 23, 25, 27, 32, 43, 44, 47, 51, 52, 53, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 19, 21, 22, 23, 24, 25, 27, 32, 44, 46, 51, 52, 53, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 19, 21, 22, 25, 27, 33, 38, 45, 47, 50, 51, 52, 59, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 19, 21, 22, 24, 25, 27, 33, 38, 43, 45, 46, 50, 51, 52, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 19, 21, 22, 23, 25, 27, 33, 38, 43, 44, 47, 50, 51, 52, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 19, 21, 22, 23, 24, 25, 27, 33, 38, 44, 46, 50, 51, 52, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 24, 25, 28, 31, 38, 41, 45, 49, 50, 53, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 24, 25, 28, 31, 33, 38, 41, 43, 45, 49, 50, 54, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 23, 28, 31, 33, 38, 41, 43, 45, 47, 48, 49, 50, 54, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 23, 24, 28, 31, 33, 38, 41, 45, 46, 48, 49, 50, 54, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 22, 28, 30, 34, 36, 41, 42, 43, 48, 50, 53, 55, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 22, 23, 26, 28, 30, 41, 42, 46, 47, 50, 53, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 22, 23, 24, 28, 30, 33, 41, 42, 43, 45, 47, 48, 50, 54, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 22, 24, 25, 27, 28, 42, 45, 47, 50, 52, 53, 54, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 22, 24, 25, 27, 28, 33, 42, 43, 45, 47, 50, 52, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 22, 23, 26, 27, 28, 42, 43, 47, 50, 52, 53, 54, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 22, 23, 24, 26, 27, 28, 42, 46, 50, 52, 53, 54, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 27, 28, 43, 44, 45, 47, 48, 52, 53, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 25, 28, 45, 46, 47, 49, 50, 52, 53, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 25, 27, 28, 43, 45, 46, 47, 52, 53, 60, 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, 28, 43, 45, 49, 50, 52, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 25, 27, 28, 45, 52, 53, 58, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 28, 43, 47, 48, 49, 50, 52, 53, 58, 60, 61, 63 ], [ 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, 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, 28, 30, 43, 48, 50, 53, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 22, 28, 30, 33, 34, 37, 41, 42, 43, 48, 50, 54, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 21, 22, 28, 31, 33, 35, 37, 38, 41, 43, 48, 49, 50, 53, 56, 59 ], [ 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, 22, 26, 27, 28, 33, 37, 42, 50, 52, 53, 55, 56, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 22, 28, 31, 35, 36, 38, 41, 43, 48, 49, 50, 54, 59, 63 ], [ 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 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 22, 26, 27, 28, 36, 42, 50, 52, 54, 55, 58, 59, 63 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 192 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS118[6], DS118[11], DS118[18], DS118[20], DS118[22], DS118[23], DS118[27], DS118[31], DS118[32], DS118[33], DS118[34], DS118[35], DS118[38], DS118[42], DS118[44], DS118[45], DS118[46], DS118[47], DS118[48], DS118[49], DS118[50], DS118[51], DS118[52], DS118[53], DS118[54], DS118[56], DS118[57], DS118[58], DS118[60], DS118[61], DS118[62], DS118[63], DS118[64], DS118[67], DS118[68], DS118[69], DS118[70], DS118[71], DS118[74], DS118[75], DS118[81], DS118[82], DS118[84], DS118[91], DS118[92], DS118[95], DS118[100], DS118[101], DS118[102], DS118[104], DS118[105], DS118[106], DS118[107], DS118[110], DS118[111], DS118[112], DS118[113], DS118[114], DS118[115], DS118[116], DS118[117], DS118[119], DS118[121], DS118[122], DS118[124], DS118[126], DS118[131], DS118[132], DS118[134], DS118[137], DS118[138], DS118[139], DS118[140], DS118[143], DS118[144], DS118[146], DS118[147], DS118[148], DS118[149], DS118[150], DS118[151], DS118[152], DS118[154], DS118[158], DS118[159], DS118[161], DS118[162], DS118[163], DS118[165], DS118[166], DS118[167], DS118[168], DS118[170], DS118[171], DS118[173], DS118[174], DS118[175], DS118[177], DS118[180], DS118[181], DS118[182], DS118[183], DS118[184], DS118[185], DS118[188], DS118[190], DS118[191], DS118[192], DS118[194], DS118[196], DS118[198], DS118[199], DS118[200], DS118[201], DS118[202], DS118[203], DS118[204], DS118[205], DS118[206], DS118[207], DS118[209], DS118[210], DS118[211], DS118[213], DS118[214], DS118[215], DS118[216], DS118[217], DS118[218], DS118[219], DS118[220], DS118[221], DS118[222], DS118[223], DS118[224], DS118[225], DS118[227], DS118[229], DS118[232], DS118[234], DS118[235], DS118[236], DS118[237], DS118[238], DS118[239], DS118[240], DS118[242], DS118[246], DS118[247], DS118[248], DS118[249], DS118[250], DS118[251], DS118[253], DS118[255], DS118[256], DS118[258], DS118[260], DS118[261], DS118[263], DS118[264], DS118[266], DS118[270], DS118[272], DS118[273], DS118[276], DS118[277], DS118[278], DS118[280], DS118[284], DS118[285], DS118[288], DS118[290], DS118[291], DS118[293], DS118[294], DS118[295], DS118[296], DS118[299], DS118[300], DS118[301], DS118[302], DS118[303], DS118[306], DS118[307], DS118[308], DS118[310], DS118[315], DS118[316], DS118[317], DS118[318], DS118[320]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,118]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,118] is 8 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,118] is RDS118:=[ [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 21, 22, 23, 28, 30, 33, 38, 43, 45, 46, 47, 48, 50, 53, 54, 56, 59, 62, 63 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 14, 17, 21, 22, 23, 28, 30, 38, 39, 40, 43, 45, 46, 47, 48, 50, 56, 57, 59, 62 ], [ 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 21, 22, 23, 28, 30, 34, 35, 38, 43, 45, 46, 47, 48, 50, 55, 56, 59, 62 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 14, 18, 19, 21, 22, 23, 28, 30, 38, 41, 43, 45, 46, 47, 48, 50, 56, 59, 62 ], [ 1, 2, 3, 7, 8, 9, 10, 11, 14, 20, 23, 28, 30, 33, 38, 42, 43, 45, 46, 47, 48, 50, 53, 54, 56, 59, 62, 63 ], [ 1, 2, 3, 7, 8, 9, 10, 11, 14, 17, 20, 23, 28, 30, 38, 39, 40, 42, 43, 45, 46, 47, 48, 50, 56, 57, 59, 62 ], [ 1, 2, 3, 7, 8, 9, 10, 11, 13, 14, 20, 23, 28, 30, 34, 35, 38, 42, 43, 45, 46, 47, 48, 50, 55, 56, 59, 62 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 18, 19, 20, 23, 28, 30, 38, 41, 42, 43, 45, 46, 47, 48, 50, 56, 59, 62 ] ]; ########################### ########################### ###########################