### 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 [64,142]. 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 [64,142]. # 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(64,142));' can be # used to create a list e of the elements of the group [64,142]. # In our list of (64,28,12) DSs in group [64,142], we have [1, # 2, 3, 4, 5, 6, 10, 11, 13, 18, 20, 23, 28, 30, 35, # 36, 37, 38, 40, 44, 45, 49, 51, 53, 57, 60, 62, 63]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[6], e[10], e[11], e[13], e[18], e[20], e[23], e[28], e[30], e[35], e[36], # e[37], e[38], e[40], e[44], e[45], e[49], e[51], e[53], e[57], e[60], e[62], e[63]] # where e is the list of the elements of the group [64,142] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,142));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 142] ### The number of inequivalent (64,28,12) DSs in group [64,142] is 1178 ### The list of all inequivalent (64,28,12) DSs in group [64,142] is DS142:=[ [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 18, 20, 23, 28, 30, 35, 36, 37, 38, 40, 44, 45, 49, 51, 53, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 18, 20, 23, 28, 30, 34, 35, 36, 37, 38, 40, 45, 49, 51, 55, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 16, 18, 20, 23, 28, 30, 34, 36, 40, 44, 45, 49, 51, 54, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 16, 18, 20, 23, 28, 30, 34, 35, 36, 40, 49, 51, 55, 56, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 16, 18, 20, 23, 28, 30, 34, 35, 36, 40, 44, 49, 51, 55, 56, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 16, 18, 19, 20, 23, 28, 30, 34, 36, 41, 49, 51, 54, 56, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 16, 18, 19, 20, 23, 28, 30, 34, 36, 41, 44, 49, 51, 54, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 15, 18, 20, 23, 28, 30, 35, 37, 40, 44, 45, 49, 51, 53, 56, 57, 60, 62, 63 ], [ 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62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 18, 19, 25, 31, 33, 40, 41, 45, 46, 53, 57, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 18, 19, 25, 31, 33, 39, 40, 41, 45, 46, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 25, 31, 34, 35, 39, 40, 41, 45, 46, 57, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 25, 31, 35, 39, 40, 45, 46, 55, 57, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 25, 31, 41, 45, 46, 49, 53, 54, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 25, 31, 39, 41, 45, 46, 49, 54, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 24, 30, 39, 41, 48, 50, 53, 54, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 19, 21, 22, 24, 30, 44, 48, 50, 53, 54, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 31, 32, 33, 36, 38, 40, 41, 45, 49, 52, 53, 54, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 20, 22, 25, 31, 33, 40, 41, 45, 46, 53, 54, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 20, 22, 25, 31, 33, 40, 41, 45, 46, 49, 53, 54, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 18, 19, 20, 22, 25, 31, 33, 40, 45, 46, 54, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 18, 19, 20, 22, 25, 31, 33, 40, 45, 46, 49, 54, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 31, 32, 35, 36, 38, 39, 40, 45, 49, 52, 54, 55, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 31, 32, 34, 35, 36, 38, 40, 45, 49, 52, 54, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 20, 22, 25, 31, 35, 39, 40, 45, 46, 54, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 20, 22, 25, 31, 35, 39, 40, 45, 46, 49, 54, 55, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 20, 22, 25, 31, 34, 35, 40, 45, 46, 54, 57, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 20, 22, 25, 31, 34, 35, 40, 45, 46, 49, 54, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 25, 31, 34, 35, 36, 37, 41, 45, 46, 49, 53, 54, 55, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 25, 31, 34, 35, 36, 37, 45, 46, 49, 54, 55, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 20, 21, 26, 29, 32, 34, 40, 48, 54, 57, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 20, 21, 25, 26, 29, 32, 34, 40, 46, 54, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 19, 25, 31, 36, 37, 39, 40, 41, 45, 46, 49, 55, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 19, 25, 31, 34, 36, 37, 40, 41, 45, 46, 49, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 30, 36, 38, 41, 44, 46, 49, 51, 52, 53, 54, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 27, 29, 30, 36, 38, 41, 43, 45, 46, 49, 52, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 30, 36, 38, 39, 41, 46, 49, 52, 53, 54, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 30, 34, 36, 38, 41, 44, 46, 52, 53, 54, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 28, 30, 36, 38, 44, 46, 49, 52, 54, 59, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 27, 29, 30, 36, 38, 43, 44, 45, 46, 52, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 19, 30, 33, 35, 36, 38, 41, 46, 49, 52, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 30, 33, 35, 36, 38, 44, 46, 52, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 30, 36, 37, 39, 40, 46, 49, 52, 53, 54, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 30, 34, 36, 37, 40, 44, 46, 52, 53, 54, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 19, 30, 34, 35, 36, 37, 41, 46, 49, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 18, 19, 30, 34, 35, 36, 37, 44, 46, 52, 55, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 19, 30, 33, 34, 40, 41, 44, 46, 52, 53, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 30, 33, 35, 41, 46, 49, 52, 53, 54, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 30, 33, 35, 39, 41, 44, 46, 52, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 19, 30, 33, 40, 46, 49, 52, 53, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 30, 34, 35, 40, 46, 49, 52, 53, 55, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 30, 34, 35, 39, 40, 44, 46, 52, 55, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 30, 34, 41, 44, 46, 52, 53, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 30, 46, 49, 52, 53, 54, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 25, 29, 36, 40, 42, 43, 44, 46, 48, 51, 54, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 25, 29, 34, 36, 40, 41, 42, 43, 46, 48, 53, 54, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 25, 28, 29, 36, 40, 42, 43, 46, 48, 49, 54, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 25, 27, 36, 40, 42, 44, 45, 46, 48, 49, 54, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 25, 27, 28, 36, 40, 42, 45, 46, 48, 51, 54, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 24, 29, 34, 36, 40, 41, 42, 44, 46, 47, 53, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 24, 25, 26, 29, 34, 36, 40, 41, 42, 53, 54, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 25, 33, 36, 39, 40, 42, 46, 48, 51, 54, 55, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 25, 28, 33, 34, 36, 40, 42, 46, 48, 54, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 20, 25, 29, 36, 39, 40, 42, 43, 46, 48, 54, 55, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 20, 24, 29, 36, 39, 40, 42, 44, 46, 47, 54, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 20, 24, 25, 26, 29, 36, 39, 40, 42, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 20, 25, 35, 36, 40, 41, 42, 46, 48, 51, 53, 54, 58, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 18, 20, 25, 28, 35, 36, 40, 42, 46, 48, 54, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 27, 30, 34, 36, 38, 39, 40, 45, 46, 52, 54, 55, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 30, 33, 36, 38, 40, 41, 46, 49, 52, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 27, 30, 36, 38, 40, 41, 45, 46, 52, 53, 54, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 19, 30, 33, 36, 38, 40, 44, 46, 52, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 35, 36, 38, 39, 40, 46, 49, 52, 54, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 34, 35, 36, 38, 40, 44, 46, 52, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 36, 37, 40, 41, 46, 49, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 35, 36, 37, 39, 41, 46, 49, 52, 54, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 34, 35, 36, 37, 41, 44, 46, 52, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 30, 34, 36, 37, 40, 44, 46, 52, 55, 59, 62, 63 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 595 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS142[1], DS142[2], DS142[3], DS142[6], DS142[7], DS142[8], DS142[9], DS142[12], DS142[14], DS142[15], DS142[18], DS142[20], DS142[21], DS142[22], DS142[25], DS142[26], DS142[28], DS142[29], DS142[30], DS142[31], DS142[32], DS142[34], DS142[36], DS142[38], DS142[40], DS142[42], DS142[44], DS142[45], DS142[46], DS142[48], DS142[51], DS142[52], DS142[54], DS142[55], DS142[68], DS142[69], DS142[73], DS142[76], DS142[77], DS142[78], DS142[79], DS142[80], DS142[82], DS142[83], DS142[89], DS142[90], DS142[94], DS142[95], DS142[100], DS142[103], DS142[105], DS142[106], DS142[108], DS142[109], DS142[110], DS142[111], DS142[114], DS142[120], DS142[122], DS142[124], DS142[125], DS142[126], DS142[129], DS142[131], DS142[132], DS142[134], DS142[135], DS142[137], DS142[140], DS142[142], DS142[144], DS142[147], DS142[148], DS142[149], DS142[150], DS142[152], DS142[153], DS142[158], DS142[159], DS142[160], DS142[162], DS142[164], DS142[165], DS142[166], DS142[168], DS142[172], DS142[174], DS142[175], DS142[177], DS142[179], DS142[180], DS142[183], DS142[196], DS142[203], DS142[208], DS142[215], DS142[225], DS142[233], DS142[238], DS142[246], DS142[247], DS142[250], DS142[254], DS142[256], DS142[260], DS142[276], DS142[281], DS142[283], DS142[286], DS142[287], DS142[294], DS142[301], DS142[304], DS142[307], DS142[308], DS142[309], DS142[310], DS142[311], DS142[312], DS142[314], DS142[315], DS142[316], DS142[318], DS142[323], DS142[325], DS142[326], DS142[327], DS142[328], DS142[331], DS142[332], DS142[344], DS142[351], DS142[354], DS142[356], DS142[357], DS142[358], DS142[360], DS142[362], DS142[364], DS142[365], DS142[366], DS142[367], DS142[368], DS142[369], DS142[370], DS142[371], DS142[372], DS142[373], DS142[379], DS142[380], DS142[391], DS142[397], DS142[398], DS142[400], DS142[401], DS142[402], DS142[403], DS142[406], DS142[407], DS142[408], DS142[410], DS142[411], DS142[412], DS142[415], DS142[418], DS142[421], DS142[422], DS142[425], DS142[436], DS142[441], DS142[444], DS142[448], DS142[449], DS142[450], DS142[451], DS142[452], DS142[453], DS142[454], DS142[456], DS142[457], DS142[458], DS142[459], DS142[462], DS142[464], DS142[465], DS142[466], DS142[468], DS142[469], DS142[470], DS142[472], DS142[475], DS142[476], DS142[477], DS142[478], DS142[479], DS142[480], DS142[481], DS142[482], DS142[483], DS142[484], DS142[485], DS142[486], DS142[487], DS142[488], DS142[489], DS142[490], DS142[493], DS142[498], DS142[511], DS142[512], DS142[514], DS142[515], DS142[516], DS142[517], DS142[518], DS142[519], DS142[520], DS142[521], DS142[522], DS142[526], DS142[532], DS142[533], DS142[534], DS142[535], DS142[536], DS142[537], DS142[539], DS142[540], DS142[541], DS142[542], DS142[544], DS142[545], DS142[546], DS142[547], DS142[548], DS142[549], DS142[550], DS142[552], DS142[554], DS142[555], DS142[557], DS142[558], DS142[561], DS142[563], DS142[566], DS142[567], DS142[568], DS142[569], DS142[571], DS142[574], DS142[577], DS142[578], DS142[579], DS142[580], DS142[586], DS142[588], DS142[589], DS142[591], DS142[598], DS142[611], DS142[612], DS142[616], DS142[617], DS142[621], DS142[626], DS142[638], DS142[643], DS142[647], DS142[648], DS142[649], DS142[651], DS142[653], DS142[655], DS142[656], DS142[658], DS142[660], DS142[661], DS142[662], DS142[663], DS142[664], DS142[667], DS142[670], DS142[671], DS142[672], DS142[675], DS142[676], DS142[677], DS142[678], DS142[680], DS142[681], DS142[682], DS142[683], DS142[686], DS142[687], DS142[692], DS142[693], DS142[696], DS142[697], DS142[698], DS142[699], DS142[700], DS142[702], DS142[703], DS142[704], DS142[707], DS142[708], DS142[711], DS142[712], DS142[713], DS142[721], DS142[722], DS142[723], DS142[724], DS142[729], DS142[730], DS142[735], DS142[736], DS142[737], DS142[738], DS142[746], DS142[757], DS142[758], DS142[761], DS142[763], DS142[764], DS142[765], DS142[767], DS142[770], DS142[772], DS142[773], DS142[776], DS142[780], DS142[781], DS142[782], DS142[783], DS142[792], DS142[804], DS142[809], DS142[810], DS142[812], DS142[813], DS142[814], DS142[819], DS142[820], DS142[823], DS142[825], DS142[827], DS142[829], DS142[831], DS142[833], DS142[834], DS142[838], DS142[841], DS142[843], DS142[845], DS142[847], DS142[848], DS142[849], DS142[851], DS142[852], DS142[859], DS142[871], DS142[872], DS142[874], DS142[875], DS142[880], DS142[893], DS142[894], DS142[915], DS142[920], DS142[923], DS142[925], DS142[942], DS142[947], DS142[949], DS142[951], DS142[952], DS142[953], DS142[956], DS142[957], DS142[958], DS142[959], DS142[960], DS142[961], DS142[962], DS142[963], DS142[964], DS142[965], DS142[966], DS142[967], DS142[969], DS142[970], DS142[971], DS142[972], DS142[973], DS142[974], DS142[976], DS142[980], DS142[981], DS142[982], DS142[983], DS142[984], DS142[985], DS142[986], DS142[987], DS142[988], DS142[989], DS142[990], DS142[991], DS142[992], DS142[993], DS142[994], DS142[995], DS142[996], DS142[997], DS142[998], DS142[999], DS142[1000], DS142[1001], DS142[1002], DS142[1003], DS142[1004], DS142[1005], DS142[1006], DS142[1007], DS142[1008], DS142[1009], DS142[1010], DS142[1011], DS142[1012], DS142[1013], DS142[1014], DS142[1015], DS142[1016], DS142[1017], DS142[1018], DS142[1019], DS142[1020], DS142[1021], DS142[1022], DS142[1023], DS142[1025], DS142[1026], DS142[1027], DS142[1028], DS142[1029], DS142[1030], DS142[1031], DS142[1032], DS142[1033], DS142[1034], DS142[1035], DS142[1036], DS142[1037], DS142[1038], DS142[1039], DS142[1040], DS142[1041], DS142[1042], DS142[1043], DS142[1044], DS142[1045], DS142[1046], DS142[1047], DS142[1048], DS142[1049], DS142[1050], DS142[1051], DS142[1052], DS142[1053], DS142[1054], DS142[1055], DS142[1056], DS142[1057], DS142[1058], DS142[1059], DS142[1060], DS142[1061], DS142[1062], DS142[1063], DS142[1064], DS142[1065], DS142[1066], DS142[1067], DS142[1068], DS142[1069], DS142[1070], DS142[1071], DS142[1072], DS142[1073], DS142[1074], DS142[1075], DS142[1076], DS142[1077], DS142[1078], DS142[1079], DS142[1080], DS142[1081], DS142[1082], DS142[1083], DS142[1084], DS142[1085], DS142[1086], DS142[1087], DS142[1088], DS142[1089], DS142[1090], DS142[1091], DS142[1092], DS142[1093], DS142[1094], DS142[1095], DS142[1096], DS142[1097], DS142[1098], DS142[1099], DS142[1100], DS142[1101], DS142[1102], DS142[1103], DS142[1104], DS142[1105], DS142[1106], DS142[1107], DS142[1108], DS142[1109], DS142[1110], DS142[1111], DS142[1112], DS142[1113], DS142[1114], DS142[1115], DS142[1116], DS142[1117], DS142[1118], DS142[1119], DS142[1120], DS142[1121], DS142[1122], DS142[1123], DS142[1124], DS142[1125], DS142[1126], DS142[1127], DS142[1128], DS142[1129], DS142[1130], DS142[1131], DS142[1132], DS142[1133], DS142[1134], DS142[1135], DS142[1136], DS142[1137], DS142[1138], DS142[1139], DS142[1140], DS142[1141], DS142[1142], DS142[1143], DS142[1144], DS142[1145], DS142[1146], DS142[1147], DS142[1148], DS142[1149], DS142[1150], DS142[1151], DS142[1152], DS142[1153], DS142[1154], DS142[1155], DS142[1156], DS142[1157], DS142[1158], DS142[1159], DS142[1160], DS142[1161], DS142[1162], DS142[1163], DS142[1164], DS142[1165], DS142[1166], DS142[1167], DS142[1168], DS142[1169], DS142[1170], DS142[1171], DS142[1172], DS142[1173], DS142[1174], DS142[1175], DS142[1176], DS142[1177], DS142[1178]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,142]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,142] is 132 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,142] is RDS142:=[ [ 2, 4, 8, 9, 11, 12, 13, 15, 18, 26, 32, 33, 34, 36, 38, 40, 44, 45, 46, 49, 50, 51, 53, 56, 57, 58, 59, 61 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 18, 26, 27, 32, 33, 34, 36, 38, 40, 43, 44, 45, 46, 51, 53, 56, 57, 61, 62, 64 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 18, 23, 26, 32, 33, 36, 38, 40, 43, 46, 49, 50, 51, 55, 56, 57, 60, 61, 63, 64 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 18, 23, 26, 32, 33, 34, 36, 38, 40, 43, 46, 49, 50, 51, 53, 56, 57, 60, 61, 64 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 18, 23, 26, 27, 32, 33, 36, 38, 40, 46, 51, 55, 56, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 18, 23, 26, 27, 32, 33, 34, 36, 38, 40, 46, 51, 53, 56, 57, 58, 59, 60, 61, 62 ], [ 2, 4, 8, 9, 11, 12, 13, 15, 17, 18, 23, 26, 32, 33, 36, 38, 39, 46, 49, 50, 51, 55, 56, 58, 59, 60, 61, 63 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 18, 20, 22, 26, 32, 33, 34, 40, 42, 44, 45, 46, 49, 50, 51, 53, 57, 58, 59, 61 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 18, 20, 22, 26, 27, 32, 33, 34, 40, 42, 43, 44, 45, 46, 51, 53, 57, 61, 62, 64 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 18, 20, 22, 23, 26, 32, 33, 40, 42, 43, 46, 49, 50, 51, 55, 57, 60, 61, 63, 64 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 18, 20, 22, 23, 26, 32, 33, 34, 40, 42, 43, 46, 49, 50, 51, 53, 57, 60, 61, 64 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 18, 20, 22, 23, 26, 27, 32, 33, 40, 42, 46, 51, 55, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 18, 20, 22, 23, 26, 27, 32, 33, 34, 40, 42, 46, 51, 53, 57, 58, 59, 60, 61, 62 ], [ 2, 4, 6, 8, 9, 11, 12, 13, 17, 18, 20, 22, 23, 26, 32, 33, 39, 42, 46, 49, 50, 51, 55, 58, 59, 60, 61, 63 ], [ 2, 4, 5, 9, 12, 13, 15, 18, 20, 21, 30, 33, 34, 36, 38, 40, 42, 44, 45, 49, 50, 51, 52, 53, 56, 57, 58, 59 ], [ 2, 4, 5, 9, 12, 13, 15, 18, 20, 21, 23, 30, 33, 36, 38, 40, 42, 43, 49, 50, 51, 52, 55, 56, 57, 60, 63, 64 ], [ 2, 4, 5, 9, 12, 13, 15, 18, 20, 21, 23, 30, 33, 34, 36, 38, 40, 42, 43, 49, 50, 51, 52, 53, 56, 57, 60, 64 ], [ 2, 4, 5, 9, 12, 13, 15, 18, 20, 21, 23, 27, 30, 33, 36, 38, 40, 42, 51, 52, 55, 56, 57, 58, 59, 60, 62, 63 ], [ 2, 4, 5, 9, 12, 13, 15, 18, 20, 21, 23, 27, 30, 33, 34, 36, 38, 40, 42, 51, 52, 53, 56, 57, 58, 59, 60, 62 ], [ 2, 4, 5, 9, 12, 13, 15, 17, 18, 20, 21, 23, 30, 33, 36, 38, 39, 42, 49, 50, 51, 52, 55, 56, 58, 59, 60, 63 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 20, 21, 26, 27, 31, 33, 39, 40, 41, 42, 43, 44, 45, 46, 51, 55, 61, 62, 63, 64 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 20, 21, 23, 26, 31, 33, 39, 40, 41, 42, 43, 46, 49, 50, 51, 55, 60, 61, 63, 64 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 20, 21, 23, 26, 31, 33, 34, 39, 40, 41, 42, 43, 46, 49, 50, 51, 53, 60, 61, 64 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 20, 21, 23, 26, 27, 31, 33, 39, 40, 41, 42, 46, 51, 55, 58, 59, 60, 61, 62, 63 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 20, 21, 23, 26, 27, 31, 33, 34, 39, 40, 41, 42, 46, 51, 53, 58, 59, 60, 61, 62 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 18, 20, 21, 26, 27, 31, 33, 34, 40, 42, 43, 44, 45, 46, 51, 53, 57, 61, 62, 64 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 18, 20, 21, 23, 26, 31, 33, 40, 42, 43, 46, 49, 50, 51, 55, 57, 60, 61, 63, 64 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 18, 20, 21, 23, 26, 31, 33, 34, 40, 42, 43, 46, 49, 50, 51, 53, 57, 60, 61, 64 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 18, 20, 21, 23, 26, 27, 31, 33, 40, 42, 46, 51, 55, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 18, 20, 21, 23, 26, 27, 31, 33, 34, 40, 42, 46, 51, 53, 57, 58, 59, 60, 61, 62 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 17, 20, 21, 23, 26, 31, 33, 34, 41, 42, 46, 49, 50, 51, 53, 57, 58, 59, 60, 61 ], [ 2, 4, 5, 8, 9, 10, 12, 13, 17, 18, 20, 21, 23, 26, 31, 33, 39, 42, 46, 49, 50, 51, 55, 58, 59, 60, 61, 63 ], [ 2, 4, 5, 6, 9, 11, 12, 13, 15, 18, 21, 22, 32, 33, 34, 36, 38, 40, 44, 45, 49, 50, 51, 53, 56, 57, 58, 59 ], [ 2, 4, 5, 6, 9, 11, 12, 13, 15, 18, 21, 22, 23, 32, 33, 36, 38, 40, 43, 49, 50, 51, 55, 56, 57, 60, 63, 64 ], [ 2, 4, 5, 6, 9, 11, 12, 13, 15, 18, 21, 22, 23, 32, 33, 34, 36, 38, 40, 43, 49, 50, 51, 53, 56, 57, 60, 64 ], [ 2, 4, 5, 6, 9, 11, 12, 13, 15, 18, 21, 22, 23, 27, 32, 33, 36, 38, 40, 51, 55, 56, 57, 58, 59, 60, 62, 63 ], [ 2, 4, 5, 6, 9, 11, 12, 13, 15, 18, 21, 22, 23, 27, 32, 33, 34, 36, 38, 40, 51, 53, 56, 57, 58, 59, 60, 62 ], [ 2, 4, 5, 6, 9, 11, 12, 13, 15, 17, 18, 21, 22, 23, 32, 33, 36, 38, 39, 49, 50, 51, 55, 56, 58, 59, 60, 63 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 21, 22, 25, 26, 27, 31, 33, 39, 40, 41, 43, 44, 45, 48, 51, 55, 62, 63, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 21, 22, 23, 25, 26, 31, 33, 39, 40, 41, 43, 48, 49, 50, 51, 55, 60, 63, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 21, 22, 23, 25, 26, 31, 33, 34, 39, 40, 41, 43, 48, 49, 50, 51, 53, 60, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 21, 22, 23, 25, 26, 27, 31, 33, 39, 40, 41, 48, 51, 55, 58, 59, 60, 62, 63 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 21, 22, 23, 25, 26, 27, 31, 33, 34, 39, 40, 41, 48, 51, 53, 58, 59, 60, 62 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 22, 25, 26, 27, 31, 33, 34, 40, 43, 44, 45, 48, 51, 53, 57, 62, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 22, 23, 25, 26, 31, 33, 40, 43, 48, 49, 50, 51, 55, 57, 60, 63, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 22, 23, 25, 26, 31, 33, 34, 40, 43, 48, 49, 50, 51, 53, 57, 60, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 22, 23, 25, 26, 27, 31, 33, 40, 48, 51, 55, 57, 58, 59, 60, 62, 63 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 22, 23, 25, 26, 27, 31, 33, 34, 40, 48, 51, 53, 57, 58, 59, 60, 62 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 17, 21, 22, 23, 25, 26, 31, 33, 34, 41, 48, 49, 50, 51, 53, 57, 58, 59, 60 ], [ 2, 4, 5, 6, 8, 9, 10, 12, 13, 17, 18, 21, 22, 23, 25, 26, 31, 33, 39, 48, 49, 50, 51, 55, 58, 59, 60, 63 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 18, 26, 32, 33, 34, 37, 40, 44, 45, 46, 49, 50, 51, 53, 57, 58, 59, 61 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 18, 26, 27, 32, 33, 34, 37, 40, 43, 44, 45, 46, 51, 53, 57, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 18, 23, 26, 32, 33, 37, 40, 43, 46, 49, 50, 51, 55, 57, 60, 61, 63, 64 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 18, 23, 26, 32, 33, 34, 37, 40, 43, 46, 49, 50, 51, 53, 57, 60, 61, 64 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 18, 23, 26, 27, 32, 33, 37, 40, 46, 51, 55, 57, 58, 59, 60, 61, 62, 63 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 18, 23, 26, 27, 32, 33, 34, 37, 40, 46, 51, 53, 57, 58, 59, 60, 61, 62 ], [ 2, 3, 4, 8, 9, 11, 12, 13, 14, 16, 17, 18, 23, 26, 32, 33, 37, 39, 46, 49, 50, 51, 55, 58, 59, 60, 61, 63 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 17, 21, 23, 26, 32, 33, 34, 46, 49, 50, 51, 53, 55, 58, 59, 60, 61, 63 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 17, 18, 21, 23, 26, 32, 33, 39, 41, 46, 49, 50, 51, 57, 58, 59, 60, 61 ], [ 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 15, 17, 21, 23, 26, 32, 33, 36, 38, 46, 49, 50, 51, 56, 58, 59, 60, 61 ], [ 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 17, 20, 21, 22, 23, 26, 32, 33, 42, 46, 49, 50, 51, 58, 59, 60, 61 ], [ 2, 3, 4, 5, 9, 12, 13, 14, 16, 18, 20, 21, 30, 33, 34, 37, 40, 42, 44, 45, 49, 50, 51, 52, 53, 57, 58, 59 ], [ 2, 3, 4, 5, 9, 12, 13, 14, 16, 18, 20, 21, 23, 30, 33, 37, 40, 42, 43, 49, 50, 51, 52, 55, 57, 60, 63, 64 ], [ 2, 3, 4, 5, 9, 12, 13, 14, 16, 18, 20, 21, 23, 30, 33, 34, 37, 40, 42, 43, 49, 50, 51, 52, 53, 57, 60, 64 ], [ 2, 3, 4, 5, 9, 12, 13, 14, 16, 18, 20, 21, 23, 27, 30, 33, 37, 40, 42, 51, 52, 55, 57, 58, 59, 60, 62, 63 ], [ 2, 3, 4, 5, 9, 12, 13, 14, 16, 18, 20, 21, 23, 27, 30, 33, 34, 37, 40, 42, 51, 52, 53, 57, 58, 59, 60, 62 ], [ 2, 3, 4, 5, 9, 12, 13, 14, 16, 17, 18, 20, 21, 23, 30, 33, 37, 39, 42, 49, 50, 51, 52, 55, 58, 59, 60, 63 ], [ 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 16, 18, 21, 22, 32, 33, 34, 37, 40, 44, 45, 49, 50, 51, 53, 57, 58, 59 ], [ 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 16, 18, 21, 22, 23, 32, 33, 37, 40, 43, 49, 50, 51, 55, 57, 60, 63, 64 ], [ 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 16, 18, 21, 22, 23, 32, 33, 34, 37, 40, 43, 49, 50, 51, 53, 57, 60, 64 ], [ 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 16, 18, 21, 22, 23, 27, 32, 33, 37, 40, 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