### 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 [64,127]. 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 [64,127]. # 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(64,127));' can be # used to create a list e of the elements of the group [64,127]. # In our list of (64,28,12) DSs in group [64,127], we have [1, # 2, 3, 4, 5, 9, 10, 12, 13, 19, 22, 23, 31, 34, 35, # 36, 37, 38, 39, 42, 43, 44, 49, 50, 51, 55, 57, 58]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[9], e[10], e[12], e[13], e[19], e[22], e[23], e[31], e[34], e[35], e[36], # e[37], e[38], e[39], e[42], e[43], e[44], e[49], e[50], e[51], e[55], e[57], e[58]] # where e is the list of the elements of the group [64,127] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,127));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 127] ### The number of inequivalent (64,28,12) DSs in group [64,127] is 1728 ### The list of all inequivalent (64,28,12) DSs in group [64,127] is DS127:=[ [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 19, 22, 23, 31, 34, 35, 36, 37, 38, 39, 42, 43, 44, 49, 50, 51, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 18, 19, 22, 23, 31, 35, 36, 37, 38, 41, 42, 43, 44, 49, 50, 51, 53, 58, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 16, 18, 22, 23, 28, 29, 31, 34, 36, 40, 42, 43, 44, 51, 54, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 15, 19, 22, 23, 28, 31, 34, 35, 37, 39, 42, 43, 44, 50, 55, 56, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 15, 18, 19, 22, 23, 28, 31, 35, 37, 41, 42, 43, 44, 50, 53, 56, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 12, 13, 15, 16, 18, 22, 23, 29, 31, 34, 38, 40, 42, 43, 44, 49, 54, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 19, 22, 23, 31, 32, 35, 36, 37, 38, 42, 43, 44, 46, 49, 50, 51, 58, 61 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 19, 22, 23, 25, 31, 32, 35, 36, 37, 38, 42, 43, 44, 48, 49, 50, 51, 58 ], [ 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9, 10, 11, 13, 16, 18, 21, 22, 24, 25, 29, 39, 40, 44, 52, 54, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 30, 36, 39, 42, 43, 47, 50, 54, 56, 58, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 23, 30, 36, 39, 42, 44, 45, 47, 50, 54, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 22, 29, 30, 34, 39, 46, 47, 48, 54, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 22, 29, 30, 34, 39, 44, 46, 47, 48, 54, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 22, 25, 29, 30, 39, 47, 53, 54, 55, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 21, 22, 25, 29, 30, 39, 44, 47, 53, 54, 55, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 26, 28, 29, 30, 31, 32, 35, 39, 47, 50, 54, 58, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 23, 26, 27, 30, 31, 32, 35, 39, 47, 50, 54, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21, 22, 28, 29, 30, 33, 34, 37, 38, 40, 43, 47, 53, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21, 22, 23, 28, 29, 30, 33, 34, 37, 38, 40, 45, 47, 53, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 18, 19, 21, 22, 27, 31, 37, 38, 43, 44, 45, 55, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 22, 27, 28, 29, 31, 33, 34, 37, 39, 42, 45, 46, 54, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 28, 29, 31, 37, 38, 39, 43, 46, 50, 53, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 27, 31, 37, 38, 39, 44, 45, 46, 50, 53, 56, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 22, 28, 31, 37, 39, 42, 43, 45, 46, 53, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 21, 30, 38, 39, 42, 43, 44, 47, 50, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 21, 23, 30, 38, 39, 42, 45, 47, 50, 54, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 22, 27, 32, 33, 34, 37, 38, 42, 47, 49, 50, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 22, 27, 32, 33, 34, 37, 38, 42, 45, 47, 49, 50, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 18, 21, 23, 26, 29, 32, 33, 38, 40, 42, 44, 45, 56, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 22, 27, 32, 33, 34, 42, 47, 49, 50, 56, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 22, 27, 32, 33, 34, 42, 45, 47, 49, 50, 56, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 20, 23, 26, 36, 39, 40, 42, 47, 48, 53, 54, 55, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 21, 29, 33, 42, 44, 45, 46, 48, 51, 53, 57, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 21, 23, 28, 29, 33, 42, 43, 44, 46, 48, 49, 53, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 19, 20, 25, 37, 40, 41, 42, 43, 44, 45, 54, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 18, 21, 27, 28, 33, 36, 42, 44, 48, 53, 55, 56, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 26, 28, 30, 34, 39, 43, 47, 51, 52, 54, 55, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 19, 23, 26, 30, 39, 43, 47, 51, 52, 54, 55, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 23, 26, 34, 36, 40, 41, 42, 47, 48, 53, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 20, 23, 26, 35, 36, 39, 41, 42, 47, 48, 54, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 27, 30, 37, 38, 39, 44, 46, 50, 52, 53, 58, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 23, 28, 30, 37, 38, 39, 44, 45, 46, 51, 52, 53, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 23, 28, 29, 30, 37, 38, 39, 44, 46, 50, 52, 53, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 21, 27, 34, 36, 42, 44, 48, 49, 51, 55, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 20, 25, 34, 37, 39, 41, 42, 44, 45, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 20, 25, 27, 29, 33, 34, 35, 37, 42, 45, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 20, 25, 34, 37, 39, 40, 42, 43, 44, 45, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 26, 28, 29, 30, 35, 39, 44, 45, 47, 50, 52, 54, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 26, 27, 30, 35, 39, 43, 47, 50, 52, 54, 61, 62, 63, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 982 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS127[6], DS127[38], DS127[72], DS127[100], DS127[101], DS127[113], DS127[125], DS127[127], DS127[128], DS127[137], DS127[139], DS127[155], DS127[158], DS127[162], DS127[173], DS127[174], DS127[185], DS127[186], DS127[187], DS127[191], DS127[193], DS127[194], DS127[209], DS127[210], DS127[211], DS127[212], DS127[213], DS127[214], DS127[215], DS127[216], DS127[217], DS127[218], DS127[219], DS127[220], DS127[221], DS127[222], DS127[223], DS127[226], DS127[228], DS127[229], DS127[230], DS127[233], DS127[248], DS127[249], DS127[261], DS127[262], DS127[263], DS127[264], DS127[271], DS127[272], DS127[273], DS127[274], DS127[279], DS127[289], DS127[290], DS127[293], DS127[294], DS127[295], DS127[296], DS127[297], DS127[298], DS127[299], DS127[300], DS127[301], DS127[302], DS127[303], DS127[304], DS127[309], DS127[310], DS127[311], DS127[312], DS127[327], DS127[332], DS127[340], DS127[341], DS127[342], DS127[343], DS127[347], DS127[360], DS127[361], DS127[362], DS127[363], DS127[364], DS127[365], DS127[366], DS127[367], DS127[368], DS127[369], DS127[372], DS127[376], DS127[377], DS127[379], DS127[384], DS127[385], DS127[386], DS127[387], DS127[388], DS127[389], DS127[391], DS127[400], DS127[406], DS127[420], DS127[421], DS127[422], DS127[423], DS127[424], DS127[425], DS127[429], DS127[430], DS127[431], DS127[433], DS127[436], DS127[438], DS127[440], DS127[443], DS127[450], DS127[451], DS127[455], DS127[458], DS127[459], DS127[468], DS127[474], DS127[494], DS127[495], DS127[496], DS127[497], DS127[507], DS127[508], DS127[509], DS127[510], DS127[513], DS127[514], DS127[517], DS127[526], DS127[532], DS127[537], DS127[552], DS127[555], DS127[560], DS127[561], DS127[562], DS127[563], DS127[572], DS127[578], DS127[592], DS127[598], DS127[603], DS127[604], DS127[605], DS127[606], DS127[611], DS127[612], DS127[613], DS127[616], DS127[617], DS127[618], DS127[619], DS127[625], DS127[626], DS127[628], DS127[631], DS127[632], DS127[640], DS127[641], DS127[647], DS127[653], DS127[655], DS127[661], DS127[662], DS127[668], DS127[671], DS127[672], DS127[675], DS127[676], DS127[677], DS127[678], DS127[679], DS127[683], DS127[684], DS127[685], DS127[686], DS127[687], DS127[688], DS127[689], DS127[690], DS127[700], DS127[701], DS127[702], DS127[703], DS127[706], DS127[707], DS127[709], DS127[716], DS127[718], DS127[723], DS127[724], DS127[725], DS127[726], DS127[735], DS127[748], DS127[757], DS127[762], DS127[764], DS127[770], DS127[771], DS127[772], DS127[773], DS127[774], DS127[775], DS127[776], DS127[777], DS127[778], DS127[779], DS127[780], DS127[781], DS127[782], DS127[783], DS127[784], DS127[785], DS127[786], DS127[787], DS127[788], DS127[789], DS127[790], DS127[791], DS127[792], DS127[793], DS127[794], DS127[795], DS127[796], DS127[797], DS127[798], DS127[799], DS127[800], DS127[801], DS127[802], DS127[803], DS127[804], DS127[805], DS127[806], DS127[807], DS127[808], DS127[809], DS127[810], DS127[812], DS127[816], DS127[817], DS127[819], DS127[820], DS127[823], DS127[824], DS127[825], DS127[826], DS127[827], DS127[828], DS127[829], DS127[830], DS127[832], DS127[839], DS127[840], DS127[841], DS127[842], DS127[843], DS127[844], DS127[845], DS127[846], DS127[847], DS127[848], DS127[849], DS127[850], DS127[851], DS127[852], DS127[853], DS127[854], DS127[855], DS127[856], DS127[857], DS127[858], DS127[859], DS127[860], DS127[861], DS127[862], DS127[863], DS127[864], DS127[865], DS127[866], DS127[867], DS127[868], DS127[869], DS127[870], DS127[871], DS127[872], DS127[873], DS127[874], DS127[875], DS127[876], DS127[877], DS127[878], DS127[879], DS127[880], DS127[881], DS127[882], DS127[883], DS127[884], DS127[885], DS127[886], DS127[887], DS127[888], DS127[889], DS127[890], DS127[891], DS127[892], DS127[893], DS127[894], DS127[895], DS127[896], DS127[897], DS127[898], DS127[899], DS127[900], DS127[903], DS127[904], DS127[905], DS127[906], DS127[907], DS127[908], DS127[909], DS127[910], DS127[911], DS127[912], DS127[913], DS127[914], DS127[915], DS127[916], DS127[917], DS127[918], DS127[919], DS127[920], DS127[921], DS127[922], DS127[923], DS127[924], DS127[925], DS127[926], DS127[927], DS127[928], DS127[929], DS127[930], DS127[931], DS127[932], DS127[933], DS127[934], DS127[935], DS127[936], DS127[937], DS127[938], DS127[939], DS127[940], DS127[941], DS127[942], DS127[943], DS127[944], DS127[946], DS127[947], DS127[948], DS127[949], DS127[953], DS127[954], DS127[955], DS127[956], DS127[957], DS127[958], DS127[959], DS127[960], DS127[961], DS127[962], DS127[963], DS127[964], DS127[965], DS127[966], DS127[967], DS127[968], DS127[969], DS127[970], DS127[971], DS127[972], DS127[973], DS127[974], DS127[975], DS127[976], DS127[977], DS127[978], DS127[979], DS127[992], DS127[993], DS127[994], DS127[995], DS127[996], DS127[997], DS127[999], DS127[1002], DS127[1005], DS127[1006], DS127[1007], DS127[1008], DS127[1009], DS127[1010], DS127[1011], DS127[1012], DS127[1013], DS127[1014], DS127[1015], DS127[1016], DS127[1017], DS127[1018], DS127[1019], DS127[1020], DS127[1021], DS127[1022], DS127[1023], DS127[1024], DS127[1025], DS127[1026], DS127[1027], DS127[1028], DS127[1029], DS127[1030], DS127[1031], DS127[1032], DS127[1033], DS127[1034], DS127[1035], DS127[1036], DS127[1037], DS127[1038], DS127[1039], DS127[1040], DS127[1041], DS127[1042], DS127[1043], DS127[1044], DS127[1045], DS127[1046], DS127[1047], DS127[1052], DS127[1053], DS127[1054], DS127[1055], DS127[1056], DS127[1057], DS127[1058], DS127[1059], DS127[1060], DS127[1061], DS127[1062], DS127[1063], DS127[1064], DS127[1065], DS127[1066], DS127[1067], DS127[1068], DS127[1069], DS127[1070], DS127[1071], DS127[1072], DS127[1073], DS127[1075], DS127[1076], DS127[1077], DS127[1078], DS127[1079], DS127[1080], DS127[1081], DS127[1082], DS127[1083], DS127[1084], DS127[1085], DS127[1086], DS127[1087], DS127[1088], DS127[1089], DS127[1090], DS127[1091], DS127[1092], DS127[1094], DS127[1096], DS127[1097], DS127[1100], DS127[1104], DS127[1107], DS127[1108], DS127[1109], DS127[1110], DS127[1111], DS127[1112], DS127[1113], DS127[1114], DS127[1115], DS127[1116], DS127[1117], DS127[1118], DS127[1119], DS127[1120], DS127[1121], DS127[1122], DS127[1123], DS127[1124], DS127[1125], DS127[1126], DS127[1127], DS127[1128], DS127[1130], DS127[1132], DS127[1135], DS127[1136], DS127[1137], DS127[1138], DS127[1139], DS127[1140], DS127[1141], DS127[1142], DS127[1143], DS127[1144], DS127[1145], DS127[1146], DS127[1147], DS127[1148], DS127[1149], DS127[1152], DS127[1153], DS127[1154], DS127[1155], DS127[1156], DS127[1157], DS127[1158], DS127[1159], DS127[1160], DS127[1161], DS127[1162], DS127[1163], DS127[1164], DS127[1165], DS127[1166], DS127[1167], DS127[1168], DS127[1169], DS127[1170], DS127[1171], DS127[1172], DS127[1173], DS127[1174], DS127[1175], DS127[1176], DS127[1177], DS127[1178], DS127[1181], DS127[1183], DS127[1184], DS127[1185], DS127[1186], DS127[1187], DS127[1188], DS127[1193], DS127[1198], DS127[1199], DS127[1200], DS127[1201], DS127[1202], DS127[1205], DS127[1209], DS127[1212], DS127[1213], DS127[1214], DS127[1216], DS127[1217], DS127[1222], DS127[1223], DS127[1224], DS127[1225], DS127[1226], DS127[1227], DS127[1228], DS127[1229], DS127[1230], DS127[1231], DS127[1240], DS127[1241], DS127[1242], DS127[1243], DS127[1244], DS127[1245], DS127[1246], DS127[1247], DS127[1253], DS127[1254], DS127[1255], DS127[1256], DS127[1257], DS127[1258], DS127[1261], DS127[1262], DS127[1263], DS127[1264], DS127[1265], DS127[1266], DS127[1268], DS127[1269], DS127[1270], DS127[1271], DS127[1273], DS127[1277], DS127[1295], DS127[1296], DS127[1297], DS127[1298], DS127[1299], DS127[1300], DS127[1301], DS127[1302], DS127[1303], DS127[1304], DS127[1305], DS127[1306], DS127[1307], DS127[1308], DS127[1309], DS127[1310], DS127[1311], DS127[1312], DS127[1313], DS127[1314], DS127[1315], DS127[1316], DS127[1317], DS127[1318], DS127[1319], DS127[1320], DS127[1321], DS127[1322], DS127[1323], DS127[1324], DS127[1325], DS127[1326], DS127[1327], DS127[1328], DS127[1329], DS127[1330], DS127[1331], DS127[1332], DS127[1333], DS127[1334], DS127[1335], DS127[1336], DS127[1337], DS127[1338], DS127[1339], DS127[1340], DS127[1341], DS127[1342], DS127[1343], DS127[1344], DS127[1345], DS127[1346], DS127[1347], DS127[1348], DS127[1349], DS127[1350], DS127[1351], DS127[1352], DS127[1353], DS127[1354], DS127[1355], DS127[1356], DS127[1357], DS127[1358], DS127[1359], DS127[1360], DS127[1361], DS127[1362], DS127[1363], DS127[1364], DS127[1365], DS127[1366], DS127[1367], DS127[1368], DS127[1369], DS127[1370], DS127[1371], DS127[1372], DS127[1373], DS127[1374], DS127[1375], DS127[1376], DS127[1377], DS127[1378], DS127[1379], DS127[1380], DS127[1381], DS127[1382], DS127[1383], DS127[1384], DS127[1385], DS127[1386], DS127[1387], DS127[1388], DS127[1389], DS127[1390], DS127[1391], DS127[1392], DS127[1393], DS127[1394], DS127[1395], DS127[1396], DS127[1397], DS127[1398], DS127[1399], DS127[1400], DS127[1401], DS127[1402], DS127[1403], DS127[1404], DS127[1405], DS127[1406], DS127[1407], DS127[1408], DS127[1409], DS127[1410], DS127[1411], DS127[1412], DS127[1413], DS127[1414], DS127[1415], DS127[1416], DS127[1417], DS127[1418], DS127[1419], DS127[1420], DS127[1421], DS127[1422], DS127[1423], DS127[1424], DS127[1425], DS127[1426], DS127[1427], DS127[1428], DS127[1429], DS127[1430], DS127[1431], DS127[1440], DS127[1441], DS127[1442], DS127[1443], DS127[1444], DS127[1447], DS127[1448], DS127[1449], DS127[1452], DS127[1453], DS127[1454], DS127[1455], DS127[1457], DS127[1464], DS127[1465], DS127[1468], DS127[1469], DS127[1470], DS127[1471], DS127[1472], DS127[1473], DS127[1474], DS127[1475], DS127[1476], DS127[1477], DS127[1478], DS127[1479], DS127[1480], DS127[1481], DS127[1482], DS127[1483], DS127[1484], DS127[1487], DS127[1488], DS127[1489], DS127[1490], DS127[1491], DS127[1492], DS127[1493], DS127[1494], DS127[1495], DS127[1496], DS127[1497], DS127[1498], DS127[1499], DS127[1500], DS127[1501], DS127[1502], DS127[1503], DS127[1504], DS127[1505], DS127[1506], DS127[1507], DS127[1508], DS127[1509], DS127[1510], DS127[1511], DS127[1512], DS127[1513], DS127[1514], DS127[1515], DS127[1516], DS127[1517], DS127[1518], DS127[1519], DS127[1520], DS127[1521], DS127[1522], DS127[1523], DS127[1524], DS127[1525], DS127[1526], DS127[1527], DS127[1528], DS127[1529], DS127[1530], DS127[1531], DS127[1532], DS127[1533], DS127[1534], DS127[1535], DS127[1536], DS127[1537], DS127[1538], DS127[1539], DS127[1540], DS127[1541], DS127[1542], DS127[1543], DS127[1544], DS127[1545], DS127[1546], DS127[1547], DS127[1548], DS127[1549], DS127[1550], DS127[1551], DS127[1552], DS127[1553], DS127[1554], DS127[1555], DS127[1556], DS127[1557], DS127[1558], DS127[1559], DS127[1560], DS127[1561], DS127[1562], DS127[1563], DS127[1564], DS127[1565], DS127[1566], DS127[1567], DS127[1568], DS127[1569], DS127[1570], DS127[1571], DS127[1572], DS127[1573], DS127[1574], DS127[1575], DS127[1576], DS127[1577], DS127[1578], DS127[1579], DS127[1580], DS127[1581], DS127[1584], DS127[1586], DS127[1587], DS127[1588], DS127[1589], DS127[1590], DS127[1591], DS127[1592], DS127[1593], DS127[1594], DS127[1595], DS127[1596], DS127[1597], DS127[1598], DS127[1602], DS127[1603], DS127[1609], DS127[1610], DS127[1611], DS127[1612], DS127[1613], DS127[1614], DS127[1615], DS127[1616], DS127[1617], DS127[1618], DS127[1619], DS127[1620], DS127[1621], DS127[1622], DS127[1623], DS127[1624], DS127[1625], DS127[1626], DS127[1627], DS127[1628], DS127[1629], DS127[1630], DS127[1632], DS127[1633], DS127[1634], DS127[1635], DS127[1636], DS127[1637], DS127[1638], DS127[1639], DS127[1640], DS127[1641], DS127[1642], DS127[1643], DS127[1644], DS127[1645], DS127[1646], DS127[1647], DS127[1648], DS127[1649], DS127[1650], DS127[1653], DS127[1654], DS127[1655], DS127[1656], DS127[1657], DS127[1658], DS127[1659], DS127[1660], DS127[1661], DS127[1662], DS127[1663], DS127[1664], DS127[1673], DS127[1677], DS127[1678], DS127[1679], DS127[1680], DS127[1695], DS127[1696], DS127[1697], DS127[1698], DS127[1699], DS127[1700], DS127[1701], DS127[1702], DS127[1703], DS127[1705], DS127[1706], DS127[1707], DS127[1708], DS127[1709], DS127[1710], DS127[1711], DS127[1712], DS127[1713], DS127[1714], DS127[1715], DS127[1716], DS127[1717], DS127[1718], DS127[1719], DS127[1720], DS127[1721], DS127[1722], DS127[1723], DS127[1724], DS127[1725], DS127[1726], DS127[1727], DS127[1728]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,127]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,127] is 6 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,127] is RDS127:=[ [ 2, 3, 4, 7, 8, 9, 13, 14, 19, 21, 23, 27, 28, 30, 31, 32, 34, 35, 39, 43, 46, 47, 48, 49, 51, 55, 57, 62 ], [ 2, 3, 4, 7, 8, 9, 13, 14, 15, 19, 21, 23, 27, 30, 31, 32, 34, 35, 36, 38, 39, 43, 46, 47, 48, 55, 56, 57 ], [ 2, 3, 4, 6, 7, 8, 9, 13, 14, 19, 20, 21, 22, 23, 27, 30, 31, 32, 34, 35, 39, 42, 43, 46, 47, 48, 55, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 14, 19, 27, 28, 30, 31, 32, 34, 35, 39, 45, 46, 47, 48, 49, 51, 55, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 14, 15, 19, 27, 30, 31, 32, 34, 35, 36, 38, 39, 45, 46, 47, 48, 55, 56, 57, 59 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 19, 20, 22, 27, 30, 31, 32, 34, 35, 39, 42, 45, 46, 47, 48, 55, 57, 59 ] ]; ########################### ########################### ###########################