### 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 [64,136]. Also, we determine the nonisomorphic # symmetric (64,28,12) designs that rise from these DSs. # Note that there is no reversible (64,28,12) difference sets in # group [64,136]. # 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(64,136));' can be # used to create a list e of the elements of the group [64,136]. # In our list of (64,28,12) DSs in group [64,136], we have [1, # 2, 3, 4, 5, 6, 8, 13, 16, 17, 20, 24, 26, 29, 30, # 31, 32, 34, 35, 36, 41, 47, 50, 51, 55, 56, 57, 62]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[6], e[8], e[13], e[16], e[17], e[20], e[24], e[26], e[29], e[30], e[31], # e[32], e[34], e[35], e[36], e[41], e[47], e[50], e[51], e[55], e[56], e[57], e[62]] # where e is the list of the elements of the group [64,136] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,136));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 136] ### The number of inequivalent (64,28,12) DSs in group [64,136] is 1050 ### The list of all inequivalent (64,28,12) DSs in group [64,136] is DS136:=[ [ 1, 2, 3, 4, 5, 6, 8, 13, 16, 17, 20, 24, 26, 29, 30, 31, 32, 34, 35, 36, 41, 47, 50, 51, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 18, 19, 20, 23, 25, 30, 31, 32, 35, 38, 41, 43, 45, 47, 53, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 13, 14, 17, 19, 20, 25, 27, 28, 30, 31, 32, 34, 35, 38, 40, 47, 50, 51, 55, 56, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 25, 26, 28, 30, 34, 35, 39, 41, 42, 48, 49, 51, 52, 54, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 24, 26, 34, 35, 39, 41, 42, 43, 46, 47, 49, 54, 56, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 25, 26, 28, 35, 42, 46, 48, 51, 53, 54, 55, 56, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 25, 26, 28, 30, 35, 42, 48, 49, 51, 52, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 24, 26, 35, 42, 43, 46, 47, 49, 53, 54, 55, 56, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 24, 26, 27, 30, 35, 42, 47, 49, 50, 52, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 24, 25, 26, 28, 35, 42, 43, 47, 48, 51, 53, 54, 55, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 14, 15, 17, 18, 23, 26, 27, 28, 35, 42, 45, 49, 50, 51, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 24, 26, 27, 30, 34, 36, 38, 40, 41, 42, 47, 49, 50, 52, 53, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 24, 25, 26, 27, 34, 36, 38, 40, 41, 42, 44, 47, 48, 50, 53, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 12, 13, 14, 23, 25, 26, 27, 34, 36, 38, 40, 41, 42, 45, 46, 48, 50, 53, 54, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 14, 17, 19, 23, 30, 31, 33, 36, 38, 40, 42, 45, 47, 48, 53, 54, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 17, 19, 24, 25, 30, 31, 35, 36, 38, 40, 42, 43, 53, 58, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 17, 19, 23, 24, 25, 30, 31, 34, 35, 36, 38, 40, 42, 45, 55, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 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59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 20, 21, 24, 28, 29, 40, 43, 44, 46, 48, 51, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 20, 21, 24, 25, 28, 29, 32, 40, 43, 48, 53, 55, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 20, 21, 23, 26, 29, 32, 40, 46, 48, 51, 53, 55, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 20, 21, 23, 26, 28, 29, 32, 40, 48, 53, 55, 58, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 20, 21, 23, 24, 29, 40, 44, 45, 46, 48, 49, 52, 53, 55, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 20, 21, 23, 24, 28, 29, 40, 45, 46, 48, 51, 52, 53, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 20, 21, 23, 24, 28, 29, 32, 40, 45, 46, 53, 55, 58, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 25, 31, 32, 34, 40, 41, 43, 47, 48, 52, 53, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 23, 31, 32, 34, 40, 41, 45, 46, 47, 52, 53, 58, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 22, 27, 28, 31, 34, 35, 36, 42, 45, 47, 53, 55, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 21, 22, 25, 27, 34, 37, 38, 49, 51, 52, 53, 54, 55, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 20, 22, 23, 24, 31, 34, 35, 36, 49, 50, 51, 53, 55, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 21, 26, 29, 32, 33, 34, 35, 39, 40, 42, 46, 48, 53, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 21, 25, 26, 29, 32, 33, 34, 35, 39, 40, 42, 46, 53, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 20, 21, 26, 29, 32, 35, 39, 40, 48, 53, 54, 55, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 18, 20, 21, 26, 29, 32, 35, 39, 40, 46, 48, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 26, 27, 30, 34, 37, 39, 40, 46, 51, 53, 54, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 24, 25, 28, 29, 32, 40, 47, 48, 53, 55, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 23, 28, 29, 32, 40, 45, 53, 55, 57, 58, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 21, 28, 32, 34, 35, 37, 42, 50, 51, 55, 56, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 17, 20, 21, 28, 29, 32, 34, 35, 36, 37, 45, 46, 49, 55, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 27, 28, 30, 31, 32, 33, 38, 41, 44, 50, 53, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 23, 28, 30, 31, 32, 33, 38, 41, 45, 49, 53, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 31, 32, 33, 35, 38, 39, 41, 45, 52, 53, 54, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 19, 32, 34, 36, 37, 38, 40, 45, 46, 49, 50, 53, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 31, 32, 34, 35, 38, 39, 40, 45, 52, 53, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 21, 28, 32, 33, 34, 38, 42, 50, 51, 53, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 19, 22, 27, 31, 38, 41, 42, 44, 47, 53, 54, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 19, 21, 22, 25, 27, 30, 34, 37, 51, 53, 54, 55, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 17, 19, 20, 21, 32, 34, 37, 39, 43, 44, 48, 51, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 29, 32, 34, 36, 37, 40, 45, 49, 51, 57, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 20, 21, 28, 29, 32, 45, 46, 49, 53, 54, 55, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 25, 29, 46, 47, 49, 52, 53, 54, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 22, 25, 27, 35, 36, 38, 49, 51, 52, 53, 54, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 20, 22, 25, 27, 31, 36, 43, 45, 46, 48, 51, 54, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 21, 26, 29, 32, 37, 39, 41, 42, 46, 48, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 21, 25, 26, 29, 32, 37, 39, 41, 42, 46, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 20, 21, 26, 29, 32, 33, 34, 37, 39, 41, 48, 58, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 20, 21, 26, 29, 32, 33, 34, 37, 39, 41, 46, 48, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 21, 22, 30, 34, 36, 37, 48, 49, 50, 51, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 21, 22, 25, 27, 35, 39, 46, 47, 52, 55, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 21, 22, 25, 27, 35, 39, 46, 47, 52, 53, 55, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 21, 22, 24, 35, 39, 44, 46, 48, 50, 52, 55, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 21, 22, 24, 34, 35, 39, 44, 46, 48, 50, 52, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21, 29, 32, 33, 36, 38, 40, 42, 45, 51, 53, 54, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21, 27, 32, 34, 35, 38, 40, 42, 45, 49, 54, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 20, 22, 26, 27, 29, 31, 37, 41, 53, 54, 55, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 31, 32, 33, 36, 38, 40, 41, 45, 52, 53, 54, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 26, 27, 30, 33, 36, 38, 40, 41, 46, 51, 53, 54, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 19, 21, 22, 25, 27, 30, 35, 36, 51, 53, 54, 56, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 26, 27, 30, 34, 35, 38, 39, 40, 46, 51, 54, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 21, 27, 32, 34, 37, 40, 42, 45, 49, 55, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 30, 31, 32, 34, 37, 39, 40, 45, 46, 49, 55, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 20, 21, 27, 32, 34, 37, 45, 46, 49, 55, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 29, 32, 34, 36, 37, 40, 42, 45, 51, 53, 55, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 22, 29, 30, 35, 37, 41, 44, 49, 50, 55, 56, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 22, 24, 27, 29, 30, 41, 44, 45, 46, 58, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 20, 22, 26, 27, 29, 31, 34, 38, 41, 54, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 26, 27, 30, 34, 36, 37, 40, 41, 46, 51, 53, 55, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 26, 27, 30, 34, 35, 37, 39, 41, 46, 51, 54, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 34, 36, 48, 50, 51, 52, 53, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 25, 27, 30, 36, 51, 53, 55, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 19, 30, 33, 37, 38, 41, 52, 53, 55, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 18, 19, 30, 33, 34, 37, 38, 44, 49, 52, 53, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 30, 38, 41, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 30, 34, 38, 39, 41, 44, 49, 52, 53, 54, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 30, 33, 35, 36, 38, 44, 49, 52, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 20, 27, 34, 35, 42, 47, 50, 54, 55, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 20, 27, 29, 33, 34, 36, 42, 47, 51, 54, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 18, 26, 30, 35, 39, 41, 43, 44, 48, 49, 52, 54, 58, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 30, 37, 40, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 30, 34, 37, 39, 40, 44, 49, 52, 53, 54, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 18, 19, 30, 34, 35, 36, 37, 44, 49, 52, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 25, 29, 34, 36, 38, 39, 40, 47, 49, 51, 53, 54, 56, 57 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 35, 38, 40, 52, 54, 55, 56, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 34, 35, 38, 39, 40, 44, 49, 52, 54, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 30, 33, 37, 39, 41, 44, 49, 52, 54, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 30, 34, 37, 39, 40, 44, 49, 52, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 25, 29, 34, 37, 38, 39, 40, 46, 49, 51, 53, 54, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 27, 29, 34, 36, 42, 47, 51, 54, 55, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 35, 37, 41, 52, 54, 55, 56, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 34, 35, 37, 39, 41, 44, 49, 52, 54, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 30, 33, 38, 41, 52, 53, 54, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 30, 34, 38, 40, 52, 53, 55, 57, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 27, 29, 38, 42, 47, 51, 53, 54, 57, 60, 63, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 615 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS136[2], DS136[3], DS136[34], DS136[42], DS136[77], DS136[86], DS136[88], DS136[97], DS136[98], DS136[100], DS136[107], DS136[113], DS136[123], DS136[124], DS136[130], DS136[131], DS136[135], DS136[137], DS136[138], DS136[139], DS136[140], DS136[141], DS136[146], DS136[157], DS136[158], DS136[159], DS136[162], DS136[164], DS136[173], DS136[182], DS136[184], DS136[185], DS136[186], DS136[195], DS136[198], DS136[211], DS136[214], DS136[219], DS136[221], DS136[223], DS136[224], DS136[231], DS136[232], DS136[233], DS136[235], DS136[242], DS136[243], DS136[249], DS136[262], DS136[263], DS136[264], DS136[266], DS136[268], DS136[272], DS136[273], DS136[274], DS136[277], DS136[280], DS136[286], DS136[290], DS136[291], DS136[301], DS136[302], DS136[303], DS136[304], DS136[309], DS136[310], DS136[311], DS136[312], DS136[318], DS136[320], DS136[328], DS136[329], DS136[333], DS136[334], DS136[337], DS136[338], DS136[340], DS136[341], DS136[342], DS136[343], DS136[345], DS136[354], DS136[356], DS136[359], DS136[361], DS136[362], DS136[363], DS136[365], DS136[366], DS136[367], DS136[369], DS136[370], DS136[371], DS136[378], DS136[379], DS136[380], DS136[382], DS136[398], DS136[402], DS136[405], DS136[407], DS136[410], DS136[411], DS136[414], DS136[415], DS136[416], DS136[417], DS136[418], DS136[422], DS136[423], DS136[425], DS136[426], DS136[427], DS136[433], DS136[435], DS136[436], DS136[437], DS136[438], DS136[439], DS136[441], DS136[442], DS136[443], DS136[444], DS136[445], DS136[447], DS136[450], DS136[451], DS136[454], DS136[455], DS136[456], DS136[457], DS136[458], DS136[459], DS136[463], DS136[467], DS136[471], DS136[473], DS136[474], DS136[479], DS136[481], DS136[482], DS136[489], DS136[490], DS136[491], DS136[492], DS136[493], DS136[494], DS136[498], DS136[507], DS136[508], DS136[510], DS136[511], DS136[512], DS136[513], DS136[514], DS136[515], DS136[516], DS136[517], DS136[518], DS136[519], DS136[520], DS136[521], DS136[522], DS136[523], DS136[524], DS136[525], DS136[526], DS136[527], DS136[528], DS136[529], DS136[530], DS136[532], DS136[533], DS136[534], DS136[535], DS136[536], DS136[537], DS136[539], DS136[540], DS136[541], DS136[543], DS136[546], DS136[548], DS136[549], DS136[550], DS136[551], DS136[552], DS136[553], DS136[554], DS136[555], DS136[556], DS136[557], DS136[558], DS136[559], DS136[560], DS136[561], DS136[562], DS136[563], DS136[564], DS136[565], DS136[566], DS136[567], DS136[568], DS136[569], DS136[570], DS136[571], DS136[572], DS136[573], DS136[574], DS136[576], DS136[577], DS136[578], DS136[579], DS136[580], DS136[581], DS136[582], DS136[583], DS136[584], DS136[585], DS136[586], DS136[587], DS136[588], DS136[598], DS136[600], DS136[602], DS136[603], DS136[604], DS136[605], DS136[606], DS136[607], DS136[608], DS136[609], DS136[610], DS136[611], DS136[612], DS136[613], DS136[614], DS136[615], DS136[616], DS136[617], DS136[618], DS136[619], DS136[620], DS136[621], DS136[622], DS136[623], DS136[624], DS136[625], DS136[626], DS136[627], DS136[628], DS136[629], DS136[630], DS136[631], DS136[632], DS136[633], DS136[634], DS136[635], DS136[636], DS136[637], DS136[638], DS136[639], DS136[640], DS136[641], DS136[642], DS136[643], DS136[644], DS136[645], DS136[646], DS136[647], DS136[648], DS136[649], DS136[650], DS136[651], DS136[652], DS136[653], DS136[654], DS136[655], DS136[656], DS136[657], DS136[658], DS136[659], DS136[660], DS136[661], DS136[662], DS136[663], DS136[664], DS136[665], DS136[666], DS136[667], DS136[668], DS136[669], DS136[670], DS136[671], DS136[672], DS136[674], DS136[678], DS136[680], DS136[681], DS136[682], DS136[683], DS136[684], DS136[685], DS136[686], DS136[687], DS136[688], DS136[689], DS136[698], DS136[699], DS136[701], DS136[702], DS136[703], DS136[704], DS136[706], DS136[707], DS136[708], DS136[709], DS136[710], DS136[711], DS136[712], DS136[713], DS136[715], DS136[716], DS136[717], DS136[718], DS136[719], DS136[720], DS136[721], DS136[722], DS136[723], DS136[724], DS136[725], DS136[726], DS136[729], DS136[730], DS136[732], DS136[733], DS136[734], DS136[735], DS136[736], DS136[738], DS136[739], DS136[740], DS136[741], DS136[742], DS136[743], DS136[744], DS136[745], DS136[746], DS136[747], DS136[748], DS136[749], DS136[750], DS136[751], DS136[752], DS136[753], DS136[754], DS136[755], DS136[757], DS136[761], DS136[762], DS136[763], DS136[764], DS136[765], DS136[766], DS136[767], DS136[768], DS136[769], DS136[770], DS136[771], DS136[772], DS136[773], DS136[774], DS136[775], DS136[778], DS136[779], DS136[780], DS136[781], DS136[782], DS136[783], DS136[785], DS136[787], DS136[788], DS136[789], DS136[791], DS136[792], DS136[793], DS136[795], DS136[801], DS136[802], DS136[803], DS136[804], DS136[805], DS136[806], DS136[807], DS136[808], DS136[809], DS136[810], DS136[811], DS136[812], DS136[813], DS136[814], DS136[815], DS136[816], DS136[817], DS136[818], DS136[819], DS136[820], DS136[821], DS136[822], DS136[823], DS136[824], DS136[825], DS136[826], DS136[827], DS136[828], DS136[829], DS136[830], DS136[831], DS136[832], DS136[833], DS136[834], DS136[835], DS136[836], DS136[837], DS136[839], DS136[840], DS136[841], DS136[842], DS136[843], DS136[844], DS136[846], DS136[847], DS136[848], DS136[849], DS136[850], DS136[851], DS136[852], DS136[853], DS136[854], DS136[855], DS136[856], DS136[857], DS136[860], DS136[862], DS136[863], DS136[864], DS136[865], DS136[866], DS136[867], DS136[868], DS136[869], DS136[870], DS136[871], DS136[872], DS136[873], DS136[874], DS136[875], DS136[876], DS136[877], DS136[878], DS136[879], DS136[880], DS136[881], DS136[882], DS136[883], DS136[884], DS136[885], DS136[886], DS136[887], DS136[888], DS136[889], DS136[894], DS136[903], DS136[906], DS136[907], DS136[908], DS136[909], DS136[910], DS136[911], DS136[912], DS136[913], DS136[914], DS136[915], DS136[916], DS136[917], DS136[918], DS136[919], DS136[920], DS136[921], DS136[922], DS136[923], DS136[924], DS136[925], DS136[926], DS136[927], DS136[928], DS136[929], DS136[930], DS136[931], DS136[933], DS136[934], DS136[935], DS136[936], DS136[937], DS136[938], DS136[939], DS136[942], DS136[943], DS136[944], DS136[945], DS136[946], DS136[947], DS136[948], DS136[949], DS136[950], DS136[951], DS136[952], DS136[953], DS136[954], DS136[955], DS136[956], DS136[957], DS136[958], DS136[959], DS136[960], DS136[961], DS136[962], DS136[963], DS136[964], DS136[965], DS136[966], DS136[967], DS136[968], DS136[969], DS136[970], DS136[971], DS136[972], DS136[973], DS136[974], DS136[975], DS136[977], DS136[978], DS136[979], DS136[980], DS136[981], DS136[982], DS136[983], DS136[984], DS136[985], DS136[986], DS136[987], DS136[988], DS136[989], DS136[990], DS136[991], DS136[992], DS136[993], DS136[994], DS136[995], DS136[996], DS136[997], DS136[998], DS136[1000], DS136[1001], DS136[1002], DS136[1003], DS136[1004], DS136[1005], DS136[1006], DS136[1007], DS136[1008], DS136[1009], DS136[1010], DS136[1011], DS136[1012], DS136[1013], DS136[1014], DS136[1015], DS136[1016], DS136[1017], DS136[1018], DS136[1019], DS136[1020], DS136[1021], DS136[1022], DS136[1023], DS136[1024], DS136[1025], DS136[1026], DS136[1027], DS136[1028], DS136[1029], DS136[1030], DS136[1031], DS136[1032], DS136[1033], DS136[1034], DS136[1035], DS136[1036], DS136[1037], DS136[1038], DS136[1039], DS136[1040], DS136[1041], DS136[1042], DS136[1043], DS136[1044], DS136[1045], DS136[1046], DS136[1047], DS136[1048], DS136[1049], DS136[1050]. # Note that there is no reversible (64,28,12) difference sets in # group [64,136]. ########################### ########################### ###########################