### 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 [64,182]. 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 [64,182]. # 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(64,182));' can be # used to create a list e of the elements of the group [64,182]. # In our list of (64,28,12) DSs in group [64,182], we have [1, # 2, 3, 4, 5, 8, 9, 11, 14, 15, 17, 19, 22, 23, 25, # 29, 31, 36, 40, 42, 44, 45, 47, 49, 52, 60, 61, 62]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[8], e[9], e[11], e[14], e[15], e[17], e[19], e[22], e[23], e[25], e[29], # e[31], e[36], e[40], e[42], e[44], e[45], e[47], e[49], e[52], e[60], e[61], e[62]] # where e is the list of the elements of the group [64,182] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,182));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 182] ### The number of inequivalent (64,28,12) DSs in group [64,182] is 1220 ### The list of all inequivalent (64,28,12) DSs in group [64,182] is DS182:=[ [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 15, 17, 19, 22, 23, 25, 29, 31, 36, 40, 42, 44, 45, 47, 49, 52, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 14, 15, 17, 19, 22, 23, 25, 28, 29, 31, 36, 40, 42, 45, 47, 51, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 17, 19, 22, 23, 26, 28, 32, 36, 40, 42, 44, 46, 50, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 17, 18, 21, 25, 26, 28, 30, 33, 37, 39, 48, 50, 52, 55, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 17, 18, 21, 25, 26, 29, 31, 33, 37, 39, 48, 49, 52, 55, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 18, 21, 25, 29, 31, 33, 38, 39, 47, 49, 52, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18, 21, 26, 28, 32, 33, 37, 39, 46, 50, 55, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18, 21, 25, 29, 32, 33, 37, 39, 47, 49, 55, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 19, 20, 28, 29, 31, 34, 38, 39, 44, 51, 52, 54, 56, 57, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 18, 19, 20, 29, 31, 34, 38, 41, 44, 49, 52, 54, 56, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 18, 19, 20, 23, 29, 31, 34, 38, 41, 43, 45, 49, 52, 54, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 18, 19, 20, 23, 27, 29, 31, 34, 38, 41, 45, 50, 52, 54, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 17, 19, 20, 23, 29, 31, 34, 38, 40, 44, 45, 49, 52, 54, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 17, 19, 20, 23, 28, 29, 31, 34, 38, 40, 45, 51, 52, 54, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 19, 20, 23, 28, 32, 34, 38, 39, 44, 50, 53, 55, 56, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 18, 20, 23, 29, 32, 34, 38, 40, 44, 49, 53, 55, 56, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 18, 20, 23, 28, 32, 34, 38, 40, 45, 50, 53, 55, 56, 57, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 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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, 23, 26, 39, 42, 44, 45, 47, 49, 50, 51, 53, 54, 55, 57, 60 ], [ 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, 39, 42, 44, 45, 47, 50, 53, 54, 55, 57, 60, 62 ], [ 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, 18, 20, 22, 26, 34, 35, 40, 42, 43, 44, 47, 49, 50, 51, 55, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 18, 20, 22, 26, 29, 34, 35, 40, 42, 43, 44, 45, 47, 49, 55, 57, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 18, 20, 22, 23, 26, 34, 35, 40, 42, 45, 47, 49, 50, 51, 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5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 26, 30, 31, 36, 38, 39, 40, 43, 44, 51, 53, 54, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 26, 30, 31, 34, 36, 38, 40, 41, 43, 49, 53, 54, 56, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 26, 30, 31, 34, 36, 38, 39, 40, 43, 44, 51, 54, 55, 56 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 22, 26, 33, 35, 38, 39, 42, 45, 47, 48, 49, 53, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 27, 30, 32, 37, 41, 44, 46, 50, 56, 58, 59, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 27, 28, 30, 32, 34, 37, 39, 46, 50, 56, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 25, 30, 32, 33, 35, 37, 38, 39, 45, 49, 53, 57, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 30, 32, 34, 37, 40, 41, 46, 55, 56, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 28, 30, 32, 34, 37, 39, 40, 46, 53, 56, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 32, 34, 37, 38, 39, 45, 48, 52, 53, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 30, 37, 38, 44, 45, 46, 51, 52, 53, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 28, 30, 34, 37, 38, 39, 45, 46, 52, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 25, 37, 38, 39, 41, 45, 46, 48, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 25, 30, 32, 37, 38, 45, 53, 55, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 25, 37, 38, 39, 45, 46, 48, 49, 53, 57, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 841 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS182[3], DS182[5], DS182[8], DS182[9], DS182[11], DS182[16], DS182[17], DS182[19], DS182[23], DS182[25], DS182[26], DS182[27], DS182[30], DS182[31], DS182[33], DS182[36], DS182[38], DS182[49], DS182[50], DS182[54], DS182[55], DS182[57], DS182[58], DS182[60], DS182[62], DS182[63], DS182[65], DS182[66], DS182[67], DS182[68], DS182[69], DS182[70], DS182[72], DS182[73], DS182[74], DS182[76], DS182[77], DS182[80], DS182[83], DS182[84], DS182[87], DS182[89], DS182[90], DS182[91], DS182[92], DS182[93], DS182[95], DS182[96], DS182[97], DS182[98], DS182[99], DS182[100], DS182[101], DS182[102], DS182[103], DS182[104], DS182[105], DS182[108], DS182[109], DS182[110], DS182[112], DS182[118], DS182[119], DS182[120], DS182[124], DS182[125], DS182[126], DS182[127], DS182[129], DS182[136], DS182[137], DS182[138], DS182[139], DS182[140], DS182[141], DS182[142], DS182[143], DS182[144], DS182[145], DS182[146], DS182[149], DS182[150], DS182[151], DS182[152], DS182[153], DS182[156], DS182[157], DS182[160], DS182[161], DS182[167], DS182[168], DS182[173], DS182[177], DS182[178], DS182[179], DS182[183], DS182[194], DS182[196], DS182[198], DS182[199], DS182[209], DS182[210], DS182[211], DS182[213], DS182[214], DS182[215], DS182[216], DS182[219], DS182[224], DS182[226], DS182[228], DS182[229], DS182[231], DS182[233], DS182[234], DS182[236], DS182[237], DS182[239], DS182[240], DS182[242], DS182[243], DS182[244], DS182[245], DS182[250], DS182[252], DS182[253], DS182[258], DS182[259], DS182[260], DS182[261], DS182[262], DS182[265], DS182[268], DS182[276], DS182[277], DS182[278], DS182[279], DS182[281], DS182[282], DS182[283], DS182[284], DS182[286], DS182[287], DS182[288], DS182[292], DS182[293], DS182[294], DS182[296], DS182[297], DS182[298], DS182[299], DS182[300], DS182[301], DS182[302], DS182[303], DS182[305], DS182[306], DS182[307], DS182[308], DS182[311], DS182[315], DS182[316], DS182[317], DS182[318], DS182[319], DS182[322], DS182[323], DS182[324], DS182[328], DS182[331], DS182[333], DS182[334], DS182[335], DS182[336], DS182[341], DS182[343], DS182[345], DS182[347], DS182[348], DS182[357], DS182[359], DS182[364], DS182[366], DS182[369], DS182[370], DS182[373], DS182[374], DS182[376], DS182[377], DS182[379], DS182[385], DS182[386], DS182[387], DS182[389], DS182[390], DS182[391], DS182[392], DS182[393], DS182[394], DS182[396], DS182[399], DS182[401], DS182[402], DS182[404], DS182[405], DS182[406], DS182[407], DS182[414], DS182[415], DS182[416], DS182[417], DS182[418], DS182[419], DS182[420], DS182[421], DS182[422], DS182[423], DS182[424], DS182[425], DS182[426], DS182[427], DS182[428], DS182[430], DS182[433], DS182[440], DS182[441], DS182[442], DS182[443], DS182[445], DS182[447], DS182[448], DS182[450], DS182[453], DS182[454], DS182[457], DS182[458], DS182[459], DS182[461], DS182[462], DS182[463], DS182[465], DS182[466], DS182[467], DS182[468], DS182[469], DS182[470], DS182[471], DS182[472], DS182[473], DS182[474], DS182[475], DS182[476], DS182[477], DS182[478], DS182[479], DS182[480], DS182[481], DS182[482], DS182[483], DS182[491], DS182[494], DS182[496], DS182[497], DS182[498], DS182[499], DS182[502], DS182[503], DS182[505], DS182[507], DS182[509], DS182[510], DS182[511], DS182[512], DS182[513], DS182[514], DS182[516], DS182[517], DS182[520], DS182[521], DS182[522], DS182[524], DS182[529], DS182[530], DS182[531], DS182[532], DS182[534], DS182[535], DS182[536], DS182[537], DS182[541], DS182[544], DS182[545], DS182[547], DS182[548], DS182[549], DS182[550], DS182[551], DS182[552], DS182[553], DS182[554], DS182[556], DS182[557], DS182[558], DS182[559], DS182[561], DS182[562], DS182[563], DS182[565], DS182[573], DS182[575], DS182[576], DS182[577], DS182[578], DS182[580], DS182[581], DS182[584], DS182[588], DS182[592], DS182[595], DS182[596], DS182[597], DS182[598], DS182[599], DS182[600], DS182[601], DS182[602], DS182[607], DS182[608], DS182[609], DS182[610], DS182[613], DS182[614], DS182[615], DS182[616], DS182[617], DS182[619], DS182[623], DS182[624], DS182[627], DS182[628], DS182[631], DS182[636], DS182[638], DS182[643], DS182[646], DS182[650], DS182[651], DS182[652], DS182[654], DS182[655], DS182[656], DS182[658], DS182[660], DS182[661], DS182[662], DS182[663], DS182[664], DS182[668], DS182[669], DS182[671], DS182[672], DS182[673], DS182[674], DS182[676], DS182[677], DS182[678], DS182[679], DS182[680], DS182[682], DS182[683], DS182[684], DS182[685], DS182[687], DS182[690], DS182[692], DS182[693], DS182[694], DS182[695], DS182[696], DS182[697], DS182[698], DS182[699], DS182[700], DS182[701], DS182[702], DS182[703], DS182[704], DS182[705], DS182[706], DS182[707], DS182[708], DS182[709], DS182[710], DS182[711], DS182[712], DS182[713], DS182[714], DS182[715], DS182[716], DS182[717], DS182[718], DS182[719], DS182[720], DS182[721], DS182[722], DS182[723], DS182[724], DS182[725], DS182[726], DS182[727], DS182[728], DS182[729], DS182[730], DS182[731], DS182[732], DS182[733], DS182[734], DS182[736], DS182[737], DS182[738], DS182[739], DS182[742], DS182[745], DS182[746], DS182[747], DS182[748], DS182[749], DS182[750], DS182[752], DS182[753], DS182[754], DS182[755], DS182[756], DS182[757], DS182[758], DS182[759], DS182[760], DS182[761], DS182[762], DS182[763], DS182[764], DS182[765], DS182[766], DS182[771], DS182[772], DS182[773], DS182[774], DS182[776], DS182[778], DS182[779], DS182[780], DS182[781], DS182[782], DS182[783], DS182[784], DS182[785], DS182[786], DS182[787], DS182[788], DS182[789], DS182[790], DS182[791], DS182[792], DS182[793], DS182[794], DS182[795], DS182[796], DS182[801], DS182[802], DS182[803], DS182[804], DS182[805], DS182[806], DS182[807], DS182[808], DS182[809], DS182[810], DS182[811], DS182[812], DS182[813], DS182[814], DS182[815], DS182[816], DS182[817], DS182[818], DS182[819], DS182[820], DS182[821], DS182[822], DS182[823], DS182[824], DS182[827], DS182[828], DS182[829], DS182[830], DS182[831], DS182[834], DS182[839], DS182[840], DS182[841], DS182[842], DS182[843], DS182[844], DS182[845], DS182[846], DS182[847], DS182[848], DS182[849], DS182[850], DS182[851], DS182[852], DS182[853], DS182[854], DS182[855], DS182[856], DS182[857], DS182[858], DS182[859], DS182[860], DS182[861], DS182[862], DS182[864], DS182[866], DS182[868], DS182[869], DS182[870], DS182[871], DS182[872], DS182[873], DS182[874], DS182[875], DS182[876], DS182[877], DS182[878], DS182[879], DS182[880], DS182[881], DS182[882], DS182[883], DS182[884], DS182[885], DS182[886], DS182[887], DS182[888], DS182[889], DS182[890], DS182[891], DS182[892], DS182[893], DS182[894], DS182[895], DS182[897], DS182[898], DS182[899], DS182[906], DS182[907], DS182[908], DS182[909], DS182[910], DS182[911], DS182[912], DS182[913], DS182[914], DS182[915], DS182[916], DS182[917], DS182[918], DS182[919], DS182[920], DS182[921], DS182[926], DS182[927], DS182[928], DS182[929], DS182[930], DS182[931], DS182[932], DS182[933], DS182[934], DS182[935], DS182[936], DS182[937], DS182[938], DS182[939], DS182[940], DS182[941], DS182[942], DS182[943], DS182[944], DS182[945], DS182[946], DS182[947], DS182[948], DS182[949], DS182[950], DS182[951], DS182[952], DS182[953], DS182[954], DS182[956], DS182[957], DS182[958], DS182[959], DS182[960], DS182[961], DS182[962], DS182[967], DS182[968], DS182[969], DS182[970], DS182[971], DS182[972], DS182[973], DS182[974], DS182[975], DS182[976], DS182[977], DS182[978], DS182[979], DS182[982], DS182[983], DS182[984], DS182[985], DS182[986], DS182[987], DS182[988], DS182[989], DS182[990], DS182[992], DS182[994], DS182[995], DS182[996], DS182[997], DS182[998], DS182[999], DS182[1000], DS182[1001], DS182[1002], DS182[1003], DS182[1004], DS182[1005], DS182[1006], DS182[1007], DS182[1008], DS182[1009], DS182[1010], DS182[1011], DS182[1012], DS182[1013], DS182[1014], DS182[1015], DS182[1016], DS182[1017], DS182[1018], DS182[1019], DS182[1020], DS182[1021], DS182[1022], DS182[1023], DS182[1024], DS182[1025], DS182[1026], DS182[1027], DS182[1028], DS182[1030], DS182[1031], DS182[1032], DS182[1033], DS182[1034], DS182[1035], DS182[1036], DS182[1037], DS182[1038], DS182[1039], DS182[1040], DS182[1041], DS182[1043], DS182[1044], DS182[1045], DS182[1046], DS182[1047], DS182[1048], DS182[1049], DS182[1050], DS182[1051], DS182[1052], DS182[1053], DS182[1054], DS182[1055], DS182[1056], DS182[1057], DS182[1058], DS182[1059], DS182[1060], DS182[1061], DS182[1062], DS182[1063], DS182[1064], DS182[1065], DS182[1066], DS182[1067], DS182[1068], DS182[1069], DS182[1070], DS182[1071], DS182[1072], DS182[1073], DS182[1074], DS182[1075], DS182[1076], DS182[1077], DS182[1078], DS182[1079], DS182[1080], DS182[1081], DS182[1082], DS182[1083], DS182[1084], DS182[1085], DS182[1086], DS182[1087], DS182[1088], DS182[1091], DS182[1092], DS182[1093], DS182[1095], DS182[1096], DS182[1097], DS182[1098], DS182[1099], DS182[1100], DS182[1101], DS182[1102], DS182[1103], DS182[1104], DS182[1107], DS182[1108], DS182[1111], DS182[1112], DS182[1113], DS182[1114], DS182[1115], DS182[1116], DS182[1117], DS182[1118], DS182[1119], DS182[1120], DS182[1121], DS182[1122], DS182[1123], DS182[1124], DS182[1125], DS182[1127], DS182[1128], DS182[1130], DS182[1131], DS182[1132], DS182[1133], DS182[1134], DS182[1135], DS182[1136], DS182[1137], DS182[1138], DS182[1139], DS182[1140], DS182[1141], DS182[1142], DS182[1143], DS182[1144], DS182[1145], DS182[1146], DS182[1147], DS182[1148], DS182[1151], DS182[1152], DS182[1153], DS182[1154], DS182[1155], DS182[1156], DS182[1157], DS182[1158], DS182[1159], DS182[1162], DS182[1163], DS182[1164], DS182[1165], DS182[1166], DS182[1167], DS182[1168], DS182[1169], DS182[1170], DS182[1171], DS182[1172], DS182[1173], DS182[1174], DS182[1175], DS182[1176], DS182[1177], DS182[1178], DS182[1179], DS182[1180], DS182[1181], DS182[1182], DS182[1183], DS182[1184], DS182[1185], DS182[1186], DS182[1187], DS182[1188], DS182[1189], DS182[1190], DS182[1191], DS182[1192], DS182[1193], DS182[1194], DS182[1195], DS182[1196], DS182[1197], DS182[1198], DS182[1199], DS182[1200], DS182[1201], DS182[1202], DS182[1203], DS182[1204], DS182[1205], DS182[1206], DS182[1207], DS182[1208], DS182[1209], DS182[1210], DS182[1211], DS182[1212], DS182[1213], DS182[1214], DS182[1215], DS182[1216], DS182[1217], DS182[1218], DS182[1219], DS182[1220]. # Finally, We list all inequivalent reversible (64,28,12) difference # sets in group [64,182]. ### The number of inequivalent reversible (64,28,12) DSs in group [64,182] is 8 ### The list of all inequivalent reversible (64,28,12) DSs in group [64,182] is RDS182:=[ [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 18, 19, 21, 22, 24, 28, 30, 41, 44, 48, 50, 53, 54, 55, 58, 60, 61, 62, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 18, 19, 21, 22, 23, 24, 28, 30, 41, 43, 45, 48, 50, 53, 54, 55, 59, 61, 62 ], [ 2, 4, 5, 6, 8, 9, 10, 11, 13, 15, 18, 19, 21, 22, 24, 28, 30, 36, 38, 41, 48, 50, 53, 54, 55, 56, 61, 62 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 16, 18, 19, 21, 22, 24, 28, 30, 37, 41, 48, 50, 53, 54, 55, 61, 62 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 22, 24, 28, 30, 35, 39, 40, 41, 44, 48, 50, 53, 58, 60, 61, 62, 63, 64 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 22, 23, 24, 28, 30, 35, 39, 40, 41, 43, 45, 48, 50, 53, 59, 61, 62, 63 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 15, 22, 24, 28, 30, 35, 36, 38, 39, 40, 41, 48, 50, 53, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 24, 28, 30, 35, 37, 39, 40, 41, 48, 50, 53, 61, 62, 63 ] ]; ########################### ########################### ###########################