### 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 [64,155]. 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 [64,155]. # 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(64,155));' can be # used to create a list e of the elements of the group [64,155]. # In our list of (64,28,12) DSs in group [64,155], we have [1, # 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 28, 29, # 30, 34, 38, 40, 43, 45, 51, 52, 54, 56, 57, 59, 63]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[6], e[9], e[12], e[13], e[14], e[18], e[20], e[23], e[28], e[29], e[30], # e[34], e[38], e[40], e[43], e[45], e[51], e[52], e[54], e[56], e[57], e[59], e[63]] # where e is the list of the elements of the group [64,155] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,155));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 155] ### The number of inequivalent (64,28,12) DSs in group [64,155] is 578 ### The list of all inequivalent (64,28,12) DSs in group [64,155] is DS155:=[ [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 28, 29, 30, 34, 38, 40, 43, 45, 51, 52, 54, 56, 57, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 27, 29, 30, 34, 38, 40, 44, 45, 50, 52, 54, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 27, 29, 30, 34, 35, 38, 40, 44, 50, 52, 55, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 19, 20, 28, 30, 34, 38, 41, 44, 50, 52, 54, 56, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 19, 20, 23, 28, 30, 34, 38, 41, 43, 45, 50, 52, 54, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 19, 20, 23, 27, 29, 30, 34, 38, 41, 44, 50, 52, 54, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 19, 20, 23, 28, 30, 38, 40, 44, 45, 50, 52, 53, 54, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 19, 20, 23, 28, 30, 34, 38, 40, 44, 45, 50, 52, 54, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 19, 20, 23, 28, 30, 34, 35, 38, 40, 44, 50, 52, 55, 56, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 19, 20, 23, 28, 29, 30, 34, 38, 40, 51, 52, 54, 56, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 19, 20, 23, 28, 29, 30, 34, 38, 40, 44, 51, 52, 54, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 14, 19, 20, 23, 28, 29, 31, 34, 38, 39, 44, 51, 52, 53, 55, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 14, 18, 19, 20, 23, 29, 31, 34, 38, 41, 44, 49, 52, 53, 55, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 19, 20, 23, 27, 29, 31, 34, 35, 38, 39, 44, 50, 52, 55, 56, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 18, 19, 20, 23, 27, 29, 31, 35, 38, 41, 44, 50, 52, 53, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 17, 19, 20, 23, 29, 31, 34, 35, 38, 40, 44, 49, 52, 55, 56, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 17, 19, 20, 23, 28, 29, 31, 35, 38, 40, 44, 51, 52, 53, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 19, 20, 23, 27, 29, 32, 34, 38, 39, 44, 50, 54, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 28, 32, 35, 38, 40, 44, 50, 53, 56, 57, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 29, 32, 34, 38, 40, 43, 45, 49, 54, 56, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 28, 32, 35, 38, 40, 43, 45, 50, 53, 56, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 27, 29, 32, 35, 38, 40, 44, 50, 53, 56, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 27, 29, 32, 34, 38, 40, 45, 50, 54, 56, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 19, 20, 23, 29, 32, 34, 38, 40, 49, 54, 56, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 19, 20, 23, 29, 32, 34, 38, 40, 44, 49, 54, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 19, 20, 23, 28, 32, 38, 40, 45, 50, 53, 54, 55, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 19, 20, 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45, 47, 51, 53, 54, 55, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 22, 26, 28, 29, 34, 39, 42, 43, 44, 45, 47, 51, 54, 57, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 22, 23, 26, 34, 35, 39, 42, 47, 49, 50, 51, 55, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 22, 23, 26, 28, 34, 35, 39, 42, 44, 47, 50, 55, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 22, 23, 26, 28, 29, 39, 42, 47, 51, 53, 54, 55, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 22, 23, 26, 28, 29, 39, 42, 44, 47, 51, 53, 54, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 22, 23, 26, 28, 29, 34, 39, 42, 47, 51, 54, 57, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 22, 23, 26, 28, 29, 34, 39, 42, 44, 47, 51, 54, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 18, 23, 26, 29, 36, 38, 39, 40, 41, 42, 44, 45, 47, 49, 54, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 18, 23, 26, 28, 29, 36, 38, 39, 40, 41, 42, 45, 47, 51, 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5, 6, 7, 9, 13, 18, 19, 21, 23, 25, 27, 28, 31, 35, 37, 41, 42, 43, 49, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 25, 27, 31, 33, 37, 41, 42, 44, 45, 49, 53, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 25, 27, 31, 33, 34, 37, 41, 42, 44, 45, 49, 55, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 25, 27, 28, 31, 33, 37, 41, 42, 45, 51, 53, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 25, 27, 28, 31, 33, 34, 37, 41, 42, 45, 51, 55, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 23, 25, 29, 31, 33, 37, 41, 42, 44, 45, 51, 53, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 23, 25, 29, 31, 33, 37, 39, 42, 44, 45, 49, 55, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 23, 25, 29, 31, 33, 34, 37, 41, 42, 44, 45, 51, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 23, 25, 28, 29, 31, 33, 37, 41, 42, 45, 49, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 23, 25, 28, 29, 31, 33, 37, 39, 42, 45, 51, 55, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 21, 23, 25, 28, 29, 31, 33, 34, 37, 41, 42, 45, 49, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 17, 18, 21, 22, 27, 28, 33, 34, 37, 45, 46, 48, 55, 57, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 17, 18, 21, 22, 25, 27, 33, 34, 37, 45, 49, 51, 55, 57, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 17, 18, 21, 22, 23, 25, 33, 34, 37, 44, 45, 50, 51, 55, 57, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 17, 18, 21, 22, 23, 25, 28, 33, 34, 37, 45, 49, 50, 55, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 18, 21, 22, 23, 27, 34, 40, 43, 44, 46, 51, 54, 57, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 18, 21, 22, 23, 27, 28, 34, 40, 43, 46, 49, 54, 57, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 18, 21, 22, 23, 25, 27, 34, 40, 43, 44, 48, 51, 54, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 18, 21, 22, 23, 25, 27, 28, 34, 40, 43, 48, 49, 54, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 27, 28, 33, 34, 41, 42, 45, 46, 48, 58, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 25, 27, 28, 33, 41, 42, 45, 53, 55, 58, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 23, 25, 33, 41, 42, 44, 45, 50, 51, 53, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 23, 25, 28, 33, 41, 42, 45, 49, 50, 53, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 33, 43, 44, 45, 48, 50, 51, 53, 55, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 33, 34, 43, 44, 45, 48, 50, 51, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 28, 33, 43, 45, 48, 49, 50, 53, 55, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 28, 33, 34, 43, 45, 48, 49, 50, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 27, 33, 45, 48, 49, 51, 53, 55, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 27, 33, 34, 45, 48, 49, 51, 57, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 27, 28, 33, 44, 45, 48, 53, 55, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 25, 27, 28, 33, 34, 44, 45, 48, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 33, 44, 46, 50, 51, 53, 55, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 33, 39, 46, 49, 50, 51, 55, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 33, 34, 44, 46, 50, 51, 57, 58, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 28, 33, 46, 49, 50, 53, 55, 57, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 28, 33, 39, 44, 46, 50, 55, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 28, 33, 34, 46, 49, 50, 57, 59, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 25, 33, 44, 48, 50, 51, 53, 55, 57, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 25, 33, 39, 48, 49, 50, 51, 55, 58, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 25, 33, 34, 44, 48, 50, 51, 57, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 25, 28, 33, 48, 49, 50, 53, 55, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 25, 28, 33, 39, 44, 48, 50, 55, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 23, 25, 28, 33, 34, 48, 49, 50, 57, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 19, 21, 22, 23, 27, 28, 30, 31, 32, 43, 46, 47, 48, 49, 53, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 17, 18, 21, 25, 26, 29, 31, 32, 34, 35, 37, 39, 42, 53, 54, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 16, 19, 21, 22, 23, 25, 27, 28, 31, 43, 47, 49, 52, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 18, 21, 25, 26, 29, 31, 32, 33, 37, 39, 42, 55, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 24, 25, 27, 32, 37, 40, 45, 49, 51, 53, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 24, 25, 27, 28, 37, 40, 44, 45, 48, 51, 52, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 23, 24, 25, 32, 37, 40, 44, 45, 50, 51, 53, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 23, 24, 25, 28, 32, 37, 40, 45, 49, 50, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 24, 25, 27, 28, 42, 45, 48, 51, 52, 53, 55, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 24, 25, 27, 28, 32, 42, 45, 53, 55, 58, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 23, 24, 25, 32, 42, 44, 45, 50, 51, 53, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 23, 24, 25, 28, 32, 42, 45, 49, 50, 53, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 25, 27, 44, 45, 49, 51, 52, 53, 59, 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, 24, 44, 46, 48, 50, 51, 52, 53, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 30, 48, 49, 50, 51, 53, 58, 59, 60, 61, 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, 44, 48, 50, 53, 59, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 21, 22, 24, 29, 34, 35, 37, 40, 41, 44, 46, 52, 53, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 21, 22, 24, 25, 32, 34, 35, 37, 40, 41, 50, 53, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 21, 22, 24, 29, 35, 37, 39, 40, 44, 46, 52, 55, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 18, 21, 22, 24, 25, 32, 35, 37, 39, 40, 50, 55, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 24, 32, 34, 41, 42, 46, 48, 50, 53, 54, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 24, 29, 34, 41, 42, 44, 46, 52, 53, 54, 57, 61, 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, 24, 32, 39, 42, 46, 48, 50, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 18, 19, 21, 24, 29, 39, 42, 44, 46, 52, 54, 55, 61, 63, 64 ], [ 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 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 376 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS155[1], DS155[2], DS155[3], DS155[6], DS155[7], DS155[10], DS155[11], DS155[14], DS155[15], DS155[17], DS155[19], DS155[20], DS155[21], DS155[24], DS155[25], DS155[26], DS155[28], DS155[29], DS155[30], DS155[31], DS155[33], DS155[38], DS155[44], DS155[45], DS155[50], DS155[53], DS155[54], DS155[55], DS155[56], DS155[57], DS155[58], DS155[62], DS155[66], DS155[68], DS155[69], DS155[70], DS155[72], DS155[73], DS155[74], DS155[77], DS155[78], DS155[80], DS155[81], DS155[91], DS155[92], DS155[93], DS155[94], DS155[99], DS155[103], DS155[104], DS155[107], DS155[108], DS155[110], DS155[112], DS155[117], DS155[118], DS155[119], DS155[121], DS155[129], DS155[130], DS155[131], DS155[132], DS155[133], DS155[134], DS155[136], DS155[137], DS155[139], DS155[140], DS155[141], DS155[142], DS155[144], DS155[145], DS155[146], DS155[147], DS155[148], DS155[149], DS155[151], DS155[152], DS155[153], DS155[154], DS155[155], DS155[156], DS155[157], DS155[158], DS155[161], DS155[164], DS155[167], DS155[169], DS155[172], DS155[180], DS155[184], DS155[186], DS155[188], DS155[191], DS155[192], DS155[193], DS155[194], DS155[195], DS155[196], DS155[197], DS155[198], DS155[199], DS155[200], DS155[201], DS155[203], DS155[205], DS155[206], DS155[208], DS155[209], DS155[210], DS155[211], DS155[212], DS155[213], DS155[215], DS155[217], DS155[221], DS155[222], DS155[223], DS155[224], DS155[226], DS155[227], DS155[228], DS155[229], DS155[230], DS155[231], DS155[233], DS155[234], DS155[235], DS155[236], DS155[240], DS155[242], DS155[243], DS155[245], DS155[247], DS155[248], DS155[249], DS155[250], DS155[251], DS155[252], DS155[253], DS155[254], DS155[256], DS155[257], DS155[258], DS155[259], DS155[261], DS155[262], DS155[263], DS155[265], DS155[266], DS155[267], DS155[268], DS155[270], DS155[271], DS155[274], DS155[275], DS155[276], DS155[279], DS155[283], DS155[284], DS155[285], DS155[286], DS155[287], DS155[291], DS155[294], DS155[300], DS155[301], DS155[302], DS155[307], DS155[309], DS155[311], DS155[312], DS155[315], DS155[316], DS155[318], DS155[319], DS155[321], DS155[322], DS155[323], DS155[324], DS155[325], DS155[326], DS155[327], DS155[328], DS155[329], DS155[330], DS155[331], DS155[332], DS155[334], DS155[336], DS155[337], DS155[338], DS155[339], DS155[341], DS155[343], DS155[344], DS155[345], DS155[346], DS155[347], DS155[348], DS155[349], DS155[350], DS155[351], DS155[352], DS155[353], DS155[354], DS155[355], DS155[356], DS155[357], DS155[358], DS155[359], DS155[360], DS155[361], DS155[362], DS155[363], DS155[364], DS155[365], DS155[366], DS155[367], DS155[368], DS155[369], DS155[370], DS155[371], DS155[373], DS155[374], DS155[375], DS155[377], DS155[378], DS155[379], DS155[380], DS155[381], DS155[382], DS155[383], DS155[384], DS155[385], DS155[386], DS155[388], DS155[392], DS155[393], DS155[394], DS155[395], DS155[396], DS155[397], DS155[399], DS155[400], DS155[401], DS155[402], DS155[404], DS155[405], DS155[406], DS155[407], DS155[409], DS155[410], DS155[411], DS155[412], DS155[413], DS155[418], DS155[420], DS155[421], DS155[424], DS155[425], DS155[428], DS155[430], DS155[431], DS155[432], DS155[433], DS155[434], DS155[435], DS155[436], DS155[437], DS155[438], DS155[439], DS155[440], DS155[441], DS155[442], DS155[445], DS155[446], DS155[449], DS155[451], DS155[452], DS155[453], DS155[454], DS155[455], DS155[456], DS155[457], DS155[459], DS155[461], DS155[464], DS155[465], DS155[467], DS155[469], DS155[470], DS155[471], DS155[472], DS155[475], DS155[476], DS155[477], DS155[479], DS155[480], DS155[482], DS155[486], DS155[487], DS155[489], DS155[490], DS155[491], DS155[492], DS155[493], DS155[494], DS155[497], DS155[498], DS155[499], DS155[500], DS155[501], DS155[502], DS155[503], DS155[504], DS155[505], DS155[506], DS155[507], DS155[509], DS155[511], DS155[512], DS155[513], DS155[514], DS155[515], DS155[516], DS155[519], DS155[520], DS155[521], DS155[522], DS155[523], DS155[524], DS155[527], DS155[528], DS155[529], DS155[530], DS155[531], DS155[532], DS155[534], DS155[536], DS155[537], DS155[538], DS155[539], DS155[540], DS155[542], DS155[543], DS155[544], DS155[545], DS155[548], DS155[550], DS155[552], DS155[553], DS155[554], DS155[555], DS155[556], DS155[557], DS155[558], DS155[559], DS155[560], DS155[561], DS155[562], DS155[563], DS155[564], DS155[565], DS155[567], DS155[568], DS155[569], DS155[570], DS155[571], DS155[572], DS155[573], DS155[574], DS155[575], DS155[576], DS155[577], DS155[578]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,155]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,155] is 20 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,155] is RDS155:=[ [ 2, 4, 5, 8, 9, 10, 11, 15, 19, 20, 21, 23, 24, 30, 36, 38, 39, 42, 48, 49, 50, 51, 56, 57, 58, 59, 60, 61 ], [ 2, 4, 5, 8, 9, 10, 11, 15, 18, 20, 21, 23, 24, 29, 30, 36, 38, 40, 42, 48, 49, 56, 57, 58, 59, 60, 61, 62 ], [ 2, 4, 5, 8, 9, 10, 11, 13, 19, 20, 21, 23, 24, 30, 33, 35, 39, 42, 48, 49, 50, 51, 54, 57, 58, 59, 60, 61 ], [ 2, 4, 5, 8, 9, 10, 11, 13, 18, 20, 21, 23, 24, 30, 33, 35, 40, 42, 45, 48, 49, 50, 51, 54, 57, 58, 61, 64 ], [ 2, 4, 5, 8, 9, 10, 11, 13, 18, 20, 21, 23, 24, 29, 30, 33, 35, 40, 42, 48, 49, 54, 57, 58, 59, 60, 61, 62 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 15, 18, 19, 21, 22, 23, 24, 30, 36, 38, 41, 48, 49, 50, 51, 56, 58, 59, 60, 61 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 18, 19, 21, 22, 23, 24, 30, 33, 35, 41, 48, 49, 50, 51, 54, 58, 59, 60, 61 ], [ 2, 3, 4, 5, 8, 9, 10, 11, 14, 16, 19, 20, 21, 23, 24, 30, 37, 39, 42, 48, 49, 50, 51, 57, 58, 59, 60, 61 ], [ 2, 3, 4, 5, 8, 9, 10, 11, 14, 16, 18, 20, 21, 23, 24, 29, 30, 37, 40, 42, 48, 49, 57, 58, 59, 60, 61, 62 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 14, 16, 18, 19, 21, 22, 23, 24, 30, 37, 41, 48, 49, 50, 51, 58, 59, 60, 61 ], [ 1, 2, 4, 7, 8, 9, 10, 11, 15, 18, 19, 20, 23, 24, 30, 36, 38, 41, 42, 48, 49, 50, 51, 56, 58, 59, 60, 61 ], [ 1, 2, 4, 7, 8, 9, 10, 11, 13, 18, 19, 20, 23, 24, 30, 33, 35, 41, 42, 48, 49, 50, 51, 54, 58, 59, 60, 61 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 15, 19, 22, 23, 24, 30, 36, 38, 39, 48, 49, 50, 51, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 15, 18, 22, 23, 24, 29, 30, 36, 38, 40, 48, 49, 56, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 19, 22, 23, 24, 30, 33, 35, 39, 48, 49, 50, 51, 54, 57, 58, 59, 60, 61 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 18, 22, 23, 24, 30, 33, 35, 40, 45, 48, 49, 50, 51, 54, 57, 58, 61, 64 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 18, 22, 23, 24, 29, 30, 33, 35, 40, 48, 49, 54, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 16, 18, 19, 20, 23, 24, 30, 37, 41, 42, 48, 49, 50, 51, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 14, 16, 19, 22, 23, 24, 30, 37, 39, 48, 49, 50, 51, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 14, 16, 18, 22, 23, 24, 29, 30, 37, 40, 48, 49, 57, 58, 59, 60, 61, 62 ] ]; ########################### ########################### ###########################