### 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 [64,101]. 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 [64,101]. # 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(64,101));' can be # used to create a list e of the elements of the group [64,101]. # In our list of (64,28,12) DSs in group [64,101], we have [1, # 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 24, 26, 27, 29, # 31, 34, 35, 36, 44, 46, 47, 49, 51, 52, 53, 60, 61]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[8], e[11], e[13], e[15], e[16], e[17], e[24], e[26], e[27], e[29], e[31], # e[34], e[35], e[36], e[44], e[46], e[47], e[49], e[51], e[52], e[53], e[60], e[61]] # where e is the list of the elements of the group [64,101] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,101));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 101] ### The number of inequivalent (64,28,12) DSs in group [64,101] is 2024 ### The list of all inequivalent (64,28,12) DSs in group [64,101] is DS101:=[ [ 1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 24, 26, 27, 29, 31, 34, 35, 36, 44, 46, 47, 49, 51, 52, 53, 60, 61 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 24, 25, 26, 27, 29, 31, 34, 35, 36, 47, 48, 49, 51, 52, 53, 58, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 15, 16, 17, 24, 26, 29, 30, 33, 34, 36, 46, 47, 50, 51, 53, 54, 58, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 15, 16, 17, 23, 25, 26, 29, 30, 33, 34, 36, 45, 46, 48, 50, 51, 53, 54, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 14, 15, 16, 17, 26, 29, 30, 34, 36, 37, 43, 46, 50, 51, 53, 58, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 14, 15, 16, 17, 23, 25, 26, 29, 30, 34, 36, 37, 45, 48, 50, 51, 53, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 15, 16, 17, 24, 26, 29, 30, 34, 35, 36, 44, 46, 47, 50, 51, 53, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 15, 16, 17, 24, 25, 26, 29, 30, 34, 35, 36, 47, 48, 50, 51, 53, 58, 62, 64 ], [ 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9, 10, 11, 14, 16, 19, 31, 32, 33, 38, 40, 41, 45, 46, 52, 53, 55, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 19, 27, 28, 30, 34, 36, 37, 40, 41, 45, 46, 49, 55, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 25, 29, 33, 35, 38, 41, 46, 47, 49, 52, 54, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 22, 25, 27, 29, 31, 35, 42, 53, 55, 56, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 25, 29, 34, 35, 38, 40, 46, 47, 49, 52, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 21, 25, 28, 29, 32, 35, 42, 53, 55, 56, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 19, 21, 22, 26, 30, 33, 34, 35, 36, 49, 50, 51, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 19, 21, 22, 26, 28, 34, 35, 49, 50, 52, 54, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 19, 21, 22, 26, 27, 33, 35, 49, 51, 52, 55, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 19, 21, 22, 26, 27, 28, 30, 35, 36, 49, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 18, 23, 26, 32, 36, 39, 41, 45, 47, 49, 50, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 18, 23, 26, 32, 36, 39, 41, 45, 46, 47, 49, 50, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 17, 26, 28, 32, 36, 39, 40, 44, 47, 50, 51, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 17, 26, 28, 32, 36, 39, 40, 44, 46, 47, 50, 51, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 19, 30, 31, 32, 33, 34, 40, 41, 45, 46, 49, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 19, 27, 28, 30, 37, 38, 40, 41, 45, 46, 49, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 20, 22, 24, 27, 29, 31, 34, 35, 36, 37, 41, 44, 53, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 20, 21, 25, 29, 32, 35, 36, 38, 40, 43, 49, 51, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 24, 31, 32, 36, 40, 41, 44, 45, 46, 47, 52, 53, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 24, 30, 31, 32, 40, 41, 44, 45, 46, 47, 49, 56, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 24, 26, 31, 32, 36, 40, 41, 44, 48, 52, 53, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 24, 26, 30, 31, 32, 40, 41, 44, 48, 49, 56, 58, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 22, 25, 29, 31, 35, 36, 38, 42, 49, 50, 54, 56, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 22, 31, 33, 38, 41, 42, 45, 47, 49, 51, 53, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 21, 25, 31, 33, 38, 40, 42, 44, 45, 49, 51, 53, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 20, 21, 24, 29, 32, 38, 40, 44, 49, 51, 53, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 30, 31, 33, 34, 36, 39, 41, 45, 47, 51, 52, 53, 56, 59 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 22, 29, 31, 38, 42, 44, 47, 49, 50, 53, 54, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 21, 29, 32, 37, 42, 43, 48, 49, 51, 53, 55, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 20, 22, 25, 27, 29, 31, 35, 36, 41, 43, 53, 54, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 30, 31, 32, 33, 38, 40, 41, 45, 46, 49, 54, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 21, 22, 26, 30, 33, 37, 49, 50, 51, 55, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 21, 22, 26, 27, 30, 33, 34, 37, 51, 53, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 30, 31, 32, 33, 35, 38, 39, 40, 45, 46, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 20, 31, 33, 34, 38, 39, 42, 45, 47, 49, 51, 53, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 20, 21, 28, 29, 32, 36, 40, 47, 53, 54, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 18, 20, 22, 31, 33, 36, 45, 47, 49, 51, 53, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 21, 29, 32, 33, 42, 44, 47, 49, 51, 53, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 20, 22, 29, 31, 34, 35, 36, 41, 47, 49, 50, 56, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 20, 22, 27, 29, 31, 35, 36, 41, 47, 53, 55, 56, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 31, 32, 34, 36, 37, 40, 41, 45, 46, 52, 53, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 30, 31, 32, 34, 37, 40, 41, 45, 46, 49, 55, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 21, 22, 26, 34, 36, 38, 50, 51, 52, 53, 54, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 21, 22, 26, 30, 34, 38, 49, 50, 51, 54, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 30, 31, 32, 33, 35, 37, 39, 41, 45, 46, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 32, 41, 42, 45, 47, 49, 50, 53, 55, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 21, 25, 32, 40, 42, 44, 45, 49, 50, 53, 55, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 20, 22, 29, 31, 34, 41, 48, 49, 50, 53, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 31, 32, 33, 38, 39, 41, 45, 46, 49, 52, 54, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 22, 32, 34, 36, 45, 47, 49, 50, 53, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 31, 32, 34, 38, 39, 40, 45, 46, 49, 52, 55, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 21, 25, 29, 32, 34, 42, 49, 51, 53, 56, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 26, 28, 33, 49, 50, 52, 53, 55, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 26, 28, 30, 33, 36, 50, 55, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 26, 27, 34, 49, 51, 52, 53, 54, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 21, 22, 26, 27, 30, 34, 36, 51, 54, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 20, 32, 34, 39, 42, 45, 47, 49, 50, 53, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 32, 36, 39, 41, 45, 47, 49, 50, 53, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 24, 25, 26, 27, 29, 34, 39, 42, 43, 51, 54, 56, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 23, 24, 28, 29, 36, 39, 42, 44, 47, 50, 54, 55, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 23, 24, 28, 29, 36, 39, 42, 44, 46, 47, 50, 54, 55, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 25, 26, 27, 35, 36, 39, 41, 46, 47, 49, 50, 53, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 24, 25, 26, 27, 35, 39, 41, 43, 46, 49, 50, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 25, 26, 28, 35, 36, 39, 40, 46, 47, 49, 51, 53, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 24, 25, 26, 28, 35, 39, 40, 43, 46, 49, 51, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 18, 19, 30, 34, 37, 38, 40, 43, 49, 52, 53, 54, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 19, 30, 33, 37, 38, 41, 43, 49, 52, 53, 55, 60, 61, 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, 16, 17, 19, 30, 33, 34, 37, 41, 43, 49, 52, 53, 60, 61, 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, 16, 17, 19, 30, 38, 41, 43, 49, 52, 53, 54, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 30, 34, 41, 43, 49, 52, 53, 54, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 30, 33, 41, 44, 49, 52, 53, 55, 59, 61, 63 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1134 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS101[1], DS101[3], DS101[11], DS101[29], DS101[36], DS101[37], DS101[41], DS101[60], DS101[62], DS101[63], DS101[64], DS101[70], DS101[77], DS101[89], DS101[91], DS101[94], DS101[95], DS101[96], DS101[97], DS101[103], DS101[104], DS101[111], DS101[113], DS101[115], DS101[116], DS101[117], DS101[118], DS101[129], DS101[130], DS101[135], DS101[145], DS101[146], DS101[149], DS101[150], DS101[154], DS101[155], DS101[156], DS101[158], DS101[176], DS101[186], DS101[187], DS101[188], DS101[189], DS101[194], DS101[199], DS101[200], DS101[202], DS101[203], DS101[204], DS101[206], DS101[208], DS101[217], DS101[220], DS101[223], DS101[224], DS101[227], DS101[230], DS101[233], DS101[236], DS101[237], DS101[238], DS101[239], DS101[241], DS101[243], DS101[244], DS101[245], DS101[246], DS101[249], DS101[250], DS101[256], DS101[265], DS101[270], DS101[276], DS101[280], DS101[285], DS101[286], DS101[292], DS101[293], DS101[302], DS101[303], DS101[304], DS101[305], DS101[308], DS101[319], DS101[320], DS101[322], DS101[323], DS101[324], DS101[325], DS101[326], DS101[329], DS101[330], DS101[331], DS101[334], DS101[337], DS101[343], DS101[346], DS101[348], DS101[349], DS101[353], DS101[355], DS101[356], DS101[358], DS101[360], DS101[361], DS101[362], DS101[363], DS101[364], DS101[365], DS101[366], DS101[367], DS101[369], DS101[370], DS101[372], DS101[380], DS101[384], DS101[385], DS101[386], DS101[388], DS101[389], DS101[390], DS101[391], DS101[392], DS101[393], DS101[396], DS101[398], DS101[399], DS101[400], DS101[401], DS101[402], DS101[403], DS101[407], DS101[409], DS101[414], DS101[416], DS101[422], DS101[423], DS101[424], DS101[425], DS101[437], DS101[438], DS101[439], DS101[440], DS101[441], DS101[443], DS101[444], DS101[446], DS101[447], DS101[448], DS101[449], DS101[450], DS101[452], DS101[453], DS101[454], DS101[455], DS101[456], DS101[457], DS101[458], DS101[459], DS101[461], DS101[462], DS101[463], DS101[465], DS101[466], DS101[469], DS101[470], DS101[471], DS101[472], DS101[473], DS101[474], DS101[475], DS101[476], DS101[477], DS101[478], DS101[481], DS101[482], DS101[485], DS101[519], DS101[520], DS101[521], DS101[527], DS101[528], DS101[538], DS101[543], DS101[545], DS101[549], DS101[550], DS101[553], DS101[554], DS101[556], DS101[557], DS101[559], DS101[561], DS101[579], DS101[580], DS101[581], DS101[583], DS101[584], DS101[585], DS101[586], DS101[589], DS101[591], DS101[593], DS101[595], DS101[598], DS101[600], DS101[601], DS101[605], DS101[606], DS101[607], DS101[608], DS101[609], DS101[610], DS101[611], DS101[612], DS101[613], DS101[614], DS101[615], DS101[616], DS101[617], DS101[618], DS101[619], DS101[620], DS101[621], DS101[635], DS101[638], DS101[648], DS101[650], DS101[652], DS101[653], DS101[654], DS101[655], DS101[656], DS101[658], DS101[661], DS101[662], DS101[663], DS101[666], DS101[668], DS101[670], DS101[671], DS101[673], DS101[680], DS101[682], DS101[691], DS101[693], DS101[695], DS101[698], DS101[699], DS101[700], DS101[701], DS101[702], DS101[703], DS101[706], DS101[709], DS101[710], DS101[717], DS101[719], DS101[728], DS101[731], DS101[732], DS101[733], DS101[734], DS101[735], DS101[736], DS101[739], DS101[741], DS101[743], DS101[745], DS101[749], DS101[750], DS101[755], DS101[756], DS101[762], DS101[767], DS101[769], DS101[770], DS101[772], DS101[773], DS101[777], DS101[778], DS101[779], DS101[781], DS101[782], DS101[783], DS101[784], DS101[785], DS101[788], DS101[789], DS101[790], DS101[792], DS101[793], DS101[794], DS101[795], DS101[798], DS101[799], DS101[800], DS101[801], DS101[802], DS101[814], DS101[820], DS101[828], DS101[829], DS101[837], DS101[839], DS101[843], DS101[844], DS101[853], DS101[854], DS101[855], DS101[856], DS101[857], DS101[858], DS101[859], DS101[860], DS101[864], DS101[865], DS101[866], DS101[867], DS101[873], DS101[878], DS101[882], DS101[888], DS101[890], DS101[891], DS101[894], DS101[896], DS101[898], DS101[899], DS101[901], DS101[916], DS101[918], DS101[922], DS101[923], DS101[924], DS101[925], DS101[927], DS101[933], DS101[934], DS101[946], DS101[949], DS101[954], DS101[955], DS101[960], DS101[961], DS101[968], DS101[974], DS101[977], DS101[979], DS101[987], DS101[989], DS101[993], DS101[994], DS101[995], DS101[996], DS101[998], DS101[999], DS101[1001], DS101[1002], DS101[1003], DS101[1004], DS101[1005], DS101[1010], DS101[1015], DS101[1020], DS101[1021], DS101[1022], DS101[1023], DS101[1024], DS101[1025], DS101[1026], DS101[1027], DS101[1028], DS101[1029], DS101[1030], DS101[1031], DS101[1032], DS101[1033], DS101[1034], DS101[1035], DS101[1036], DS101[1037], DS101[1038], DS101[1039], DS101[1041], DS101[1042], DS101[1043], DS101[1047], DS101[1048], DS101[1049], DS101[1050], DS101[1051], DS101[1053], DS101[1054], DS101[1055], DS101[1056], DS101[1057], DS101[1059], DS101[1060], DS101[1062], DS101[1064], DS101[1068], DS101[1069], DS101[1070], DS101[1071], DS101[1072], DS101[1073], DS101[1075], DS101[1076], DS101[1078], DS101[1083], DS101[1084], DS101[1085], DS101[1086], DS101[1087], DS101[1088], DS101[1089], DS101[1090], DS101[1091], DS101[1092], DS101[1093], DS101[1095], DS101[1096], DS101[1097], DS101[1099], DS101[1100], DS101[1101], DS101[1102], DS101[1103], DS101[1104], DS101[1105], DS101[1106], DS101[1107], DS101[1110], DS101[1111], DS101[1112], DS101[1113], DS101[1114], DS101[1115], DS101[1116], DS101[1119], DS101[1120], DS101[1122], DS101[1125], DS101[1126], DS101[1127], DS101[1130], DS101[1131], DS101[1133], DS101[1134], DS101[1135], DS101[1136], DS101[1137], DS101[1138], DS101[1139], DS101[1140], DS101[1141], DS101[1142], DS101[1145], DS101[1146], DS101[1147], DS101[1148], DS101[1149], DS101[1151], DS101[1152], DS101[1153], DS101[1154], DS101[1156], DS101[1158], DS101[1159], DS101[1160], DS101[1161], DS101[1163], DS101[1164], DS101[1165], DS101[1166], DS101[1167], DS101[1168], DS101[1172], DS101[1173], DS101[1174], DS101[1176], DS101[1177], DS101[1178], DS101[1180], DS101[1181], DS101[1182], DS101[1183], DS101[1184], DS101[1185], DS101[1186], DS101[1188], DS101[1189], DS101[1190], DS101[1193], DS101[1194], DS101[1195], DS101[1196], DS101[1198], DS101[1201], DS101[1202], DS101[1203], DS101[1204], DS101[1205], DS101[1208], DS101[1209], DS101[1210], DS101[1211], DS101[1212], DS101[1213], DS101[1214], DS101[1215], DS101[1216], DS101[1217], DS101[1218], DS101[1219], DS101[1220], DS101[1221], DS101[1222], DS101[1223], DS101[1224], DS101[1225], DS101[1226], DS101[1227], DS101[1228], DS101[1229], DS101[1231], DS101[1232], DS101[1233], DS101[1236], DS101[1237], DS101[1238], DS101[1239], DS101[1243], DS101[1244], DS101[1245], DS101[1247], DS101[1248], DS101[1249], DS101[1250], DS101[1251], DS101[1252], DS101[1253], DS101[1254], DS101[1256], DS101[1257], DS101[1258], DS101[1259], DS101[1260], DS101[1261], DS101[1262], DS101[1263], DS101[1264], DS101[1265], DS101[1266], DS101[1267], DS101[1268], DS101[1269], DS101[1270], DS101[1271], DS101[1272], DS101[1273], DS101[1274], DS101[1275], DS101[1276], DS101[1277], DS101[1278], DS101[1280], DS101[1284], DS101[1285], DS101[1286], DS101[1296], DS101[1297], DS101[1298], DS101[1299], DS101[1300], DS101[1308], DS101[1311], DS101[1312], DS101[1313], DS101[1314], DS101[1315], DS101[1316], DS101[1317], DS101[1318], DS101[1319], DS101[1320], DS101[1321], DS101[1322], DS101[1323], DS101[1324], DS101[1325], DS101[1326], DS101[1327], DS101[1328], DS101[1329], DS101[1330], DS101[1333], DS101[1336], DS101[1337], DS101[1344], DS101[1345], DS101[1346], DS101[1348], DS101[1353], DS101[1357], DS101[1359], DS101[1361], DS101[1362], DS101[1363], DS101[1364], DS101[1365], DS101[1366], DS101[1367], DS101[1368], DS101[1369], DS101[1370], DS101[1371], DS101[1372], DS101[1373], DS101[1374], DS101[1375], DS101[1376], DS101[1377], DS101[1378], DS101[1379], DS101[1380], DS101[1381], DS101[1382], DS101[1383], DS101[1384], DS101[1385], DS101[1386], DS101[1387], DS101[1388], DS101[1389], DS101[1390], DS101[1391], DS101[1393], DS101[1394], DS101[1395], DS101[1396], DS101[1397], DS101[1398], DS101[1399], DS101[1400], DS101[1401], DS101[1402], DS101[1403], DS101[1404], DS101[1405], DS101[1406], DS101[1407], DS101[1408], DS101[1409], DS101[1410], DS101[1414], DS101[1416], DS101[1420], DS101[1421], DS101[1422], DS101[1423], DS101[1424], DS101[1425], DS101[1429], DS101[1430], DS101[1431], DS101[1432], DS101[1433], DS101[1434], DS101[1435], DS101[1436], DS101[1437], DS101[1438], DS101[1439], DS101[1440], DS101[1442], DS101[1443], DS101[1444], DS101[1445], DS101[1446], DS101[1447], DS101[1448], DS101[1449], DS101[1450], DS101[1451], DS101[1452], DS101[1453], DS101[1454], DS101[1455], DS101[1457], DS101[1458], DS101[1459], DS101[1460], DS101[1461], DS101[1462], DS101[1463], DS101[1464], DS101[1465], DS101[1466], DS101[1467], DS101[1468], DS101[1469], DS101[1471], DS101[1473], DS101[1474], DS101[1475], DS101[1476], DS101[1477], DS101[1478], DS101[1479], DS101[1480], DS101[1481], DS101[1482], DS101[1483], DS101[1484], DS101[1485], DS101[1486], DS101[1487], DS101[1488], DS101[1489], DS101[1490], DS101[1491], DS101[1492], DS101[1493], DS101[1494], DS101[1495], DS101[1496], DS101[1497], DS101[1498], DS101[1499], DS101[1500], DS101[1501], DS101[1502], DS101[1503], DS101[1505], DS101[1506], DS101[1507], DS101[1508], DS101[1509], DS101[1510], DS101[1511], DS101[1512], DS101[1513], DS101[1514], DS101[1515], DS101[1517], DS101[1518], DS101[1519], DS101[1520], DS101[1521], DS101[1522], DS101[1523], DS101[1524], DS101[1525], DS101[1526], DS101[1527], DS101[1528], DS101[1529], DS101[1530], DS101[1539], DS101[1540], DS101[1541], DS101[1542], DS101[1543], DS101[1544], DS101[1545], DS101[1546], DS101[1547], DS101[1548], DS101[1549], DS101[1550], DS101[1551], DS101[1552], DS101[1553], DS101[1554], DS101[1557], DS101[1558], DS101[1561], DS101[1562], DS101[1563], DS101[1564], DS101[1565], DS101[1566], DS101[1567], DS101[1568], DS101[1569], DS101[1570], DS101[1571], DS101[1572], DS101[1573], DS101[1574], DS101[1575], DS101[1576], DS101[1577], DS101[1579], DS101[1580], DS101[1582], DS101[1584], DS101[1585], DS101[1586], DS101[1587], DS101[1588], DS101[1589], DS101[1590], DS101[1591], DS101[1592], DS101[1593], DS101[1594], DS101[1595], DS101[1596], DS101[1597], DS101[1610], DS101[1611], DS101[1612], DS101[1613], DS101[1614], DS101[1615], DS101[1616], DS101[1617], DS101[1618], DS101[1619], DS101[1620], DS101[1621], DS101[1622], DS101[1623], DS101[1624], DS101[1625], DS101[1626], DS101[1627], DS101[1628], DS101[1629], DS101[1630], DS101[1631], DS101[1632], DS101[1634], DS101[1635], DS101[1636], DS101[1637], DS101[1638], DS101[1640], DS101[1641], DS101[1642], DS101[1644], DS101[1645], DS101[1646], DS101[1648], DS101[1649], DS101[1650], DS101[1651], DS101[1652], DS101[1653], DS101[1654], DS101[1655], DS101[1656], DS101[1657], DS101[1658], DS101[1659], DS101[1660], DS101[1661], DS101[1662], DS101[1663], DS101[1664], DS101[1665], DS101[1666], DS101[1667], DS101[1668], DS101[1673], DS101[1681], DS101[1683], DS101[1685], DS101[1686], DS101[1688], DS101[1689], DS101[1691], DS101[1692], DS101[1693], DS101[1694], DS101[1695], DS101[1696], DS101[1698], DS101[1699], DS101[1700], DS101[1701], DS101[1702], DS101[1703], DS101[1705], DS101[1706], DS101[1707], DS101[1708], DS101[1709], DS101[1710], DS101[1711], DS101[1712], DS101[1714], DS101[1715], DS101[1716], DS101[1717], DS101[1719], DS101[1720], DS101[1721], DS101[1722], DS101[1723], DS101[1724], DS101[1726], DS101[1727], DS101[1730], DS101[1731], DS101[1732], DS101[1733], DS101[1734], DS101[1735], DS101[1736], DS101[1743], DS101[1745], DS101[1746], DS101[1747], DS101[1748], DS101[1749], DS101[1750], DS101[1751], DS101[1752], DS101[1753], DS101[1756], DS101[1757], DS101[1758], DS101[1759], DS101[1760], DS101[1761], DS101[1762], DS101[1763], DS101[1764], DS101[1765], DS101[1766], DS101[1767], DS101[1769], DS101[1770], DS101[1771], DS101[1772], DS101[1773], DS101[1775], DS101[1776], DS101[1777], DS101[1778], DS101[1779], DS101[1780], DS101[1781], DS101[1782], DS101[1783], DS101[1784], DS101[1785], DS101[1786], DS101[1788], DS101[1790], DS101[1791], DS101[1792], DS101[1793], DS101[1794], DS101[1795], DS101[1796], DS101[1797], DS101[1798], DS101[1799], DS101[1800], DS101[1801], DS101[1802], DS101[1804], DS101[1805], DS101[1806], DS101[1807], DS101[1808], DS101[1809], DS101[1810], DS101[1811], DS101[1812], DS101[1813], DS101[1814], DS101[1816], DS101[1817], DS101[1818], DS101[1819], DS101[1820], DS101[1821], DS101[1822], DS101[1823], DS101[1824], DS101[1825], DS101[1826], DS101[1827], DS101[1828], DS101[1829], DS101[1830], DS101[1831], DS101[1832], DS101[1834], DS101[1836], DS101[1838], DS101[1841], DS101[1842], DS101[1843], DS101[1844], DS101[1845], DS101[1846], DS101[1847], DS101[1848], DS101[1849], DS101[1850], DS101[1851], DS101[1853], DS101[1854], DS101[1855], DS101[1857], DS101[1858], DS101[1859], DS101[1860], DS101[1861], DS101[1862], DS101[1863], DS101[1864], DS101[1865], DS101[1866], DS101[1867], DS101[1868], DS101[1869], DS101[1870], DS101[1871], DS101[1872], DS101[1873], DS101[1874], DS101[1875], DS101[1876], DS101[1877], DS101[1878], DS101[1879], DS101[1880], DS101[1881], DS101[1882], DS101[1884], DS101[1885], DS101[1887], DS101[1889], DS101[1895], DS101[1901], DS101[1906], DS101[1914], DS101[1915], DS101[1916], DS101[1917], DS101[1918], DS101[1919], DS101[1920], DS101[1921], DS101[1922], DS101[1923], DS101[1924], DS101[1925], DS101[1926], DS101[1927], DS101[1928], DS101[1929], DS101[1930], DS101[1931], DS101[1932], DS101[1933], DS101[1934], DS101[1935], DS101[1938], DS101[1939], DS101[1940], DS101[1941], DS101[1942], DS101[1943], DS101[1945], DS101[1946], DS101[1947], DS101[1948], DS101[1949], DS101[1950], DS101[1952], DS101[1954], DS101[1955], DS101[1956], DS101[1957], DS101[1962], DS101[1963], DS101[1966], DS101[1968], DS101[1969], DS101[1970], DS101[1971], DS101[1972], DS101[1973], DS101[1974], DS101[1975], DS101[1976], DS101[1977], DS101[1978], DS101[1979], DS101[1980], DS101[1981], DS101[1985], DS101[1986], DS101[1987], DS101[1988], DS101[1989], DS101[1990], DS101[1991], DS101[1992], DS101[1993], DS101[1996], DS101[1997], DS101[1998], DS101[1999], DS101[2000], DS101[2001], DS101[2002], DS101[2003], DS101[2006], DS101[2008], DS101[2009], DS101[2010], DS101[2011], DS101[2012], DS101[2013], DS101[2014], DS101[2015], DS101[2016], DS101[2017], DS101[2018], DS101[2019], DS101[2020], DS101[2021], DS101[2023], DS101[2024]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,101]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,101] is 560 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,101] is RDS101:=[ [ 2, 5, 8, 9, 10, 15, 17, 18, 21, 25, 27, 32, 38, 39, 40, 41, 43, 45, 47, 51, 52, 53, 57, 58, 60, 61, 62, 63 ], [ 2, 5, 8, 9, 10, 15, 17, 18, 21, 24, 27, 32, 38, 39, 40, 41, 44, 45, 48, 51, 52, 53, 57, 58, 59, 61, 62, 63 ], [ 2, 5, 8, 9, 10, 15, 17, 18, 20, 21, 25, 27, 32, 36, 38, 40, 41, 42, 43, 45, 47, 51, 52, 56, 58, 60, 61, 62 ], [ 2, 5, 8, 9, 10, 15, 17, 18, 20, 21, 24, 27, 32, 36, 38, 40, 41, 42, 44, 45, 48, 51, 52, 56, 58, 59, 61, 62 ], [ 2, 5, 6, 8, 9, 10, 15, 17, 21, 22, 25, 27, 32, 36, 38, 39, 40, 43, 45, 47, 51, 52, 56, 57, 58, 60, 61, 62 ], [ 2, 5, 6, 8, 9, 10, 15, 17, 21, 22, 24, 27, 32, 36, 38, 39, 40, 44, 45, 48, 51, 52, 56, 57, 58, 59, 61, 62 ], [ 2, 5, 6, 8, 9, 10, 15, 17, 20, 21, 22, 25, 27, 32, 38, 40, 42, 43, 45, 47, 51, 52, 53, 58, 60, 61, 62, 63 ], [ 2, 5, 6, 8, 9, 10, 15, 17, 20, 21, 22, 24, 27, 32, 38, 40, 42, 44, 45, 48, 51, 52, 53, 58, 59, 61, 62, 63 ], [ 2, 4, 8, 9, 10, 17, 18, 19, 20, 25, 27, 32, 36, 40, 41, 42, 43, 45, 47, 51, 52, 53, 56, 58, 60, 61, 62, 63 ], [ 2, 4, 8, 9, 10, 17, 18, 19, 20, 24, 27, 32, 36, 40, 41, 42, 44, 45, 48, 51, 52, 53, 56, 58, 59, 61, 62, 63 ], [ 2, 4, 8, 9, 10, 15, 17, 19, 20, 25, 27, 32, 38, 39, 40, 42, 43, 45, 47, 51, 52, 53, 57, 58, 60, 61, 62, 63 ], [ 2, 4, 8, 9, 10, 15, 17, 19, 20, 24, 27, 32, 38, 39, 40, 42, 44, 45, 48, 51, 52, 53, 57, 58, 59, 61, 62, 63 ], [ 2, 4, 8, 9, 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