### 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 [64,120]. 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 [64,120]. # 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(64,120));' can be # used to create a list e of the elements of the group [64,120]. # In our list of (64,28,12) DSs in group [64,120], we have [1, # 2, 3, 4, 5, 6, 9, 12, 14, 15, 20, 23, 24, 27, 30, # 36, 39, 40, 41, 43, 45, 46, 47, 51, 52, 59, 61, 62]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[6], e[9], e[12], e[14], e[15], e[20], e[23], e[24], e[27], e[30], e[36], # e[39], e[40], e[41], e[43], e[45], e[46], e[47], e[51], e[52], e[59], e[61], e[62]] # where e is the list of the elements of the group [64,120] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,120));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 120] ### The number of inequivalent (64,28,12) DSs in group [64,120] is 2672 ### The list of all inequivalent (64,28,12) DSs in group [64,120] is DS120:=[ [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 20, 23, 24, 27, 30, 36, 39, 40, 41, 43, 45, 46, 47, 51, 52, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 20, 23, 24, 27, 29, 30, 39, 40, 41, 43, 44, 46, 47, 50, 52, 56, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 17, 20, 23, 24, 27, 30, 36, 41, 43, 45, 46, 47, 51, 52, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 17, 19, 20, 23, 24, 30, 40, 43, 44, 46, 47, 49, 50, 51, 52, 56, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 17, 19, 20, 23, 24, 27, 30, 36, 40, 46, 47, 51, 52, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 14, 15, 17, 19, 20, 23, 24, 27, 30, 36, 40, 43, 46, 47, 51, 52, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 17, 19, 23, 27, 32, 35, 36, 37, 38, 40, 42, 44, 49, 51, 53, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 17, 19, 20, 23, 27, 32, 35, 36, 37, 38, 40, 43, 44, 49, 51, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 16, 20, 23, 27, 32, 35, 37, 39, 40, 41, 43, 44, 49, 51, 53, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 19, 20, 23, 24, 27, 29, 32, 36, 38, 39, 43, 44, 46, 47, 50, 52, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 17, 19, 20, 23, 24, 29, 32, 36, 38, 40, 43, 44, 46, 47, 49, 52, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 16, 20, 23, 27, 28, 32, 33, 37, 39, 40, 41, 45, 49, 52, 53, 54, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 16, 19, 20, 23, 27, 28, 32, 33, 37, 39, 43, 49, 52, 53, 54, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 16, 19, 20, 23, 24, 28, 32, 37, 39, 43, 46, 47, 50, 52, 57, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 16, 19, 20, 23, 24, 27, 28, 32, 37, 39, 43, 46, 47, 49, 52, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 16, 17, 20, 27, 28, 32, 33, 37, 41, 43, 44, 49, 52, 53, 54, 57, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 14, 16, 17, 20, 24, 27, 28, 32, 37, 41, 43, 44, 46, 47, 49, 52, 57, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 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45, 49, 54, 55, 56, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 23, 29, 36, 37, 38, 39, 40, 43, 49, 51, 54, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 29, 33, 38, 42, 45, 46, 51, 53, 54, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 29, 33, 38, 40, 42, 46, 50, 51, 53, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 29, 33, 38, 40, 42, 43, 50, 51, 53, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 27, 29, 38, 42, 44, 47, 51, 53, 54, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 24, 29, 33, 38, 39, 42, 50, 51, 53, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 27, 29, 38, 40, 43, 44, 51, 53, 54, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 23, 29, 33, 38, 43, 49, 51, 54, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 19, 23, 33, 37, 38, 39, 41, 46, 49, 50, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 29, 37, 38, 39, 40, 43, 50, 51, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 29, 36, 37, 38, 39, 40, 46, 50, 51, 53, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 29, 34, 37, 39, 46, 48, 51, 53, 54, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 26, 29, 33, 34, 39, 40, 46, 50, 51, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 20, 21, 29, 33, 38, 46, 50, 51, 53, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 27, 37, 38, 41, 44, 46, 50, 53, 56, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 27, 31, 38, 41, 52, 53, 54, 59, 60, 61, 63 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1743 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS120[1], DS120[2], DS120[9], DS120[10], DS120[11], DS120[13], DS120[14], DS120[15], DS120[17], DS120[19], DS120[22], DS120[24], DS120[25], DS120[28], DS120[37], DS120[38], DS120[39], DS120[40], DS120[41], DS120[46], DS120[47], DS120[48], DS120[49], DS120[50], DS120[53], DS120[56], DS120[57], DS120[63], DS120[67], DS120[68], DS120[70], DS120[79], DS120[81], DS120[84], DS120[85], DS120[90], DS120[93], DS120[96], DS120[97], DS120[103], DS120[106], DS120[107], DS120[108], DS120[109], DS120[111], DS120[112], DS120[114], DS120[119], DS120[127], DS120[131], DS120[133], DS120[147], DS120[152], DS120[160], DS120[162], DS120[163], DS120[164], DS120[169], DS120[170], DS120[171], DS120[172], DS120[175], DS120[176], DS120[180], DS120[181], DS120[182], DS120[191], DS120[200], DS120[203], DS120[206], DS120[211], DS120[212], DS120[213], DS120[214], DS120[221], DS120[222], DS120[230], DS120[232], DS120[236], DS120[239], DS120[240], DS120[241], DS120[245], DS120[247], DS120[249], DS120[251], DS120[253], DS120[256], DS120[258], DS120[259], DS120[262], DS120[267], DS120[279], DS120[284], DS120[287], DS120[288], DS120[289], DS120[290], DS120[293], DS120[300], DS120[305], DS120[306], DS120[308], DS120[309], DS120[318], DS120[321], DS120[322], DS120[323], DS120[325], DS120[326], DS120[329], DS120[331], DS120[332], DS120[337], DS120[338], DS120[341], DS120[344], DS120[346], DS120[347], DS120[355], DS120[356], DS120[357], DS120[360], DS120[366], DS120[367], DS120[368], DS120[369], DS120[372], DS120[373], DS120[376], DS120[377], DS120[378], DS120[379], DS120[380], DS120[382], DS120[388], DS120[389], DS120[390], DS120[392], DS120[394], DS120[395], DS120[396], DS120[397], DS120[399], DS120[400], DS120[405], DS120[406], DS120[408], DS120[409], DS120[411], DS120[415], DS120[416], DS120[417], DS120[418], DS120[419], DS120[420], DS120[421], DS120[422], DS120[423], DS120[424], DS120[425], DS120[426], DS120[427], DS120[428], DS120[429], DS120[431], DS120[441], DS120[442], DS120[443], DS120[444], DS120[446], DS120[447], DS120[454], DS120[457], DS120[458], DS120[459], DS120[461], DS120[462], DS120[463], DS120[464], DS120[466], DS120[475], DS120[482], DS120[484], DS120[486], DS120[499], DS120[500], DS120[501], DS120[502], DS120[504], DS120[506], DS120[511], DS120[512], DS120[516], DS120[520], DS120[521], DS120[522], DS120[523], DS120[537], DS120[539], DS120[544], DS120[545], DS120[546], DS120[552], DS120[555], DS120[564], DS120[567], DS120[570], DS120[571], DS120[572], DS120[573], DS120[574], DS120[575], DS120[576], DS120[577], DS120[578], DS120[579], DS120[580], DS120[581], DS120[582], DS120[583], DS120[584], DS120[590], DS120[599], DS120[600], DS120[602], DS120[603], DS120[604], DS120[605], DS120[615], DS120[626], DS120[627], DS120[628], DS120[629], DS120[631], DS120[633], DS120[635], DS120[637], DS120[644], DS120[646], DS120[647], DS120[652], DS120[658], DS120[660], DS120[661], DS120[663], DS120[664], DS120[665], DS120[666], DS120[673], DS120[678], DS120[682], DS120[683], DS120[687], DS120[688], DS120[691], DS120[694], DS120[695], DS120[696], DS120[697], DS120[701], DS120[702], DS120[708], DS120[711], DS120[714], DS120[716], DS120[724], DS120[725], DS120[726], DS120[729], DS120[731], DS120[733], DS120[734], DS120[736], DS120[737], DS120[738], DS120[739], DS120[745], DS120[747], DS120[748], DS120[749], DS120[750], DS120[753], DS120[754], DS120[760], DS120[762], DS120[774], DS120[775], DS120[776], DS120[778], DS120[779], DS120[782], DS120[783], DS120[784], DS120[785], DS120[791], DS120[793], DS120[795], DS120[796], DS120[797], DS120[798], DS120[799], DS120[800], DS120[801], DS120[804], DS120[807], DS120[809], DS120[810], DS120[811], DS120[812], DS120[813], DS120[814], DS120[821], DS120[824], DS120[825], DS120[826], DS120[829], DS120[830], DS120[831], DS120[833], DS120[834], DS120[835], DS120[837], DS120[838], DS120[839], DS120[840], DS120[841], DS120[842], DS120[845], DS120[846], DS120[848], DS120[849], DS120[850], DS120[851], DS120[854], DS120[855], DS120[858], DS120[859], DS120[860], DS120[861], DS120[862], DS120[863], DS120[864], DS120[865], DS120[867], DS120[869], DS120[871], DS120[872], DS120[873], DS120[876], DS120[878], DS120[879], DS120[880], DS120[881], DS120[884], DS120[885], DS120[886], DS120[887], DS120[888], DS120[890], DS120[892], DS120[893], DS120[894], DS120[895], DS120[896], DS120[897], DS120[898], DS120[899], DS120[902], DS120[903], DS120[904], DS120[906], DS120[907], DS120[908], DS120[913], DS120[914], DS120[915], DS120[916], DS120[917], DS120[918], DS120[919], DS120[920], DS120[921], DS120[922], DS120[925], DS120[927], DS120[930], DS120[932], DS120[934], DS120[939], DS120[943], DS120[944], DS120[945], DS120[946], DS120[947], DS120[951], DS120[954], DS120[956], DS120[957], DS120[959], DS120[963], DS120[965], DS120[968], DS120[969], DS120[970], DS120[971], DS120[972], DS120[973], DS120[974], DS120[975], DS120[976], DS120[977], DS120[978], DS120[979], DS120[980], DS120[981], DS120[982], DS120[983], DS120[984], DS120[985], DS120[986], DS120[987], DS120[989], DS120[999], DS120[1001], DS120[1002], DS120[1003], DS120[1004], DS120[1008], DS120[1009], DS120[1012], DS120[1014], DS120[1015], DS120[1016], DS120[1017], DS120[1018], DS120[1022], DS120[1024], DS120[1026], DS120[1029], DS120[1031], DS120[1032], DS120[1033], DS120[1034], DS120[1035], DS120[1039], DS120[1041], DS120[1042], DS120[1043], DS120[1044], DS120[1045], DS120[1046], DS120[1051], DS120[1057], DS120[1060], DS120[1062], DS120[1063], DS120[1064], DS120[1065], DS120[1066], DS120[1067], DS120[1068], DS120[1069], DS120[1070], DS120[1071], DS120[1072], DS120[1073], DS120[1078], DS120[1079], DS120[1080], DS120[1081], DS120[1082], DS120[1084], DS120[1086], DS120[1087], DS120[1088], DS120[1089], DS120[1090], DS120[1091], DS120[1092], DS120[1093], DS120[1094], DS120[1095], DS120[1096], DS120[1097], DS120[1101], DS120[1104], DS120[1108], DS120[1109], DS120[1110], DS120[1111], DS120[1112], DS120[1113], DS120[1114], DS120[1115], DS120[1116], DS120[1117], DS120[1118], DS120[1120], DS120[1121], DS120[1122], DS120[1123], DS120[1131], DS120[1132], DS120[1134], DS120[1135], DS120[1136], DS120[1137], DS120[1140], DS120[1141], DS120[1142], DS120[1143], DS120[1144], DS120[1145], DS120[1147], DS120[1148], DS120[1149], DS120[1153], DS120[1154], DS120[1155], DS120[1160], DS120[1161], DS120[1162], DS120[1163], DS120[1164], DS120[1166], DS120[1167], DS120[1171], DS120[1173], DS120[1174], DS120[1175], DS120[1179], DS120[1180], DS120[1181], DS120[1182], DS120[1183], DS120[1184], DS120[1185], DS120[1186], DS120[1187], DS120[1190], DS120[1192], DS120[1193], DS120[1194], DS120[1195], DS120[1200], DS120[1201], DS120[1202], DS120[1204], DS120[1207], DS120[1212], DS120[1214], DS120[1220], DS120[1223], DS120[1225], DS120[1227], DS120[1228], DS120[1229], DS120[1230], DS120[1231], DS120[1232], DS120[1233], DS120[1234], DS120[1239], DS120[1240], DS120[1241], DS120[1242], DS120[1243], DS120[1244], DS120[1245], DS120[1246], DS120[1247], DS120[1248], DS120[1249], DS120[1251], DS120[1252], DS120[1253], DS120[1254], DS120[1255], DS120[1256], DS120[1257], DS120[1258], DS120[1259], DS120[1260], DS120[1261], DS120[1262], DS120[1263], DS120[1264], DS120[1265], DS120[1267], DS120[1268], DS120[1269], DS120[1276], DS120[1277], DS120[1278], DS120[1280], DS120[1281], DS120[1282], DS120[1283], DS120[1285], DS120[1288], DS120[1289], DS120[1290], DS120[1291], DS120[1292], DS120[1293], DS120[1294], DS120[1302], DS120[1304], DS120[1305], DS120[1306], DS120[1307], DS120[1308], DS120[1309], DS120[1313], DS120[1316], DS120[1317], DS120[1318], DS120[1319], DS120[1320], DS120[1321], DS120[1323], DS120[1324], DS120[1325], DS120[1326], DS120[1328], DS120[1330], DS120[1332], DS120[1335], DS120[1336], DS120[1337], DS120[1338], DS120[1344], DS120[1349], DS120[1350], DS120[1351], DS120[1352], DS120[1354], DS120[1356], DS120[1357], DS120[1358], DS120[1364], DS120[1367], DS120[1368], DS120[1369], DS120[1370], DS120[1371], DS120[1372], DS120[1374], DS120[1375], DS120[1376], DS120[1377], DS120[1378], DS120[1379], DS120[1382], DS120[1384], DS120[1385], DS120[1388], DS120[1389], DS120[1390], DS120[1391], DS120[1392], DS120[1393], DS120[1395], DS120[1402], DS120[1403], DS120[1404], DS120[1405], DS120[1406], DS120[1407], DS120[1411], DS120[1412], DS120[1413], DS120[1414], DS120[1415], DS120[1416], DS120[1417], DS120[1418], DS120[1419], DS120[1420], DS120[1421], DS120[1422], DS120[1423], DS120[1424], DS120[1425], DS120[1426], DS120[1427], DS120[1428], DS120[1429], DS120[1430], DS120[1431], DS120[1432], DS120[1433], DS120[1434], DS120[1435], DS120[1436], DS120[1437], DS120[1438], DS120[1439], DS120[1440], DS120[1441], DS120[1442], DS120[1443], DS120[1444], DS120[1445], DS120[1446], DS120[1450], DS120[1460], DS120[1461], DS120[1462], DS120[1463], DS120[1464], DS120[1466], DS120[1467], DS120[1468], DS120[1469], DS120[1470], DS120[1471], DS120[1472], DS120[1473], DS120[1474], DS120[1475], DS120[1476], DS120[1477], DS120[1478], DS120[1479], DS120[1480], DS120[1481], DS120[1482], DS120[1483], DS120[1484], DS120[1485], DS120[1486], DS120[1487], DS120[1503], DS120[1504], DS120[1506], DS120[1508], DS120[1509], DS120[1510], DS120[1512], DS120[1514], DS120[1515], DS120[1516], DS120[1517], DS120[1518], DS120[1519], DS120[1521], DS120[1522], DS120[1525], DS120[1526], DS120[1527], DS120[1528], DS120[1529], DS120[1530], DS120[1531], DS120[1532], DS120[1533], DS120[1534], DS120[1535], DS120[1536], DS120[1543], DS120[1547], DS120[1557], DS120[1558], DS120[1559], DS120[1560], DS120[1561], DS120[1562], DS120[1563], DS120[1564], DS120[1565], DS120[1566], DS120[1567], DS120[1568], DS120[1569], DS120[1570], DS120[1571], DS120[1572], DS120[1573], DS120[1574], DS120[1575], DS120[1584], DS120[1588], DS120[1589], DS120[1590], DS120[1591], DS120[1592], DS120[1593], DS120[1594], DS120[1595], DS120[1596], DS120[1597], DS120[1598], DS120[1599], DS120[1600], DS120[1601], DS120[1602], DS120[1603], DS120[1604], DS120[1605], DS120[1606], DS120[1607], DS120[1608], DS120[1609], DS120[1610], DS120[1611], DS120[1612], DS120[1613], DS120[1614], DS120[1615], DS120[1616], DS120[1617], DS120[1618], DS120[1619], DS120[1620], DS120[1621], DS120[1622], DS120[1623], DS120[1624], DS120[1625], DS120[1626], DS120[1627], DS120[1628], DS120[1629], DS120[1630], DS120[1631], DS120[1632], DS120[1633], DS120[1634], DS120[1635], DS120[1636], DS120[1637], DS120[1638], DS120[1639], DS120[1640], DS120[1643], DS120[1644], DS120[1645], DS120[1646], DS120[1647], DS120[1648], DS120[1649], DS120[1650], DS120[1651], DS120[1652], DS120[1653], DS120[1654], DS120[1655], DS120[1656], DS120[1657], DS120[1658], DS120[1659], DS120[1660], DS120[1661], DS120[1662], DS120[1663], DS120[1664], DS120[1665], DS120[1666], DS120[1667], DS120[1668], DS120[1669], DS120[1670], DS120[1671], DS120[1672], DS120[1673], DS120[1674], DS120[1675], DS120[1676], DS120[1677], DS120[1678], DS120[1679], DS120[1680], DS120[1681], DS120[1687], DS120[1696], DS120[1698], DS120[1699], DS120[1700], DS120[1702], DS120[1703], DS120[1704], DS120[1705], DS120[1706], 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DS120[2662], DS120[2663], DS120[2664], DS120[2665], DS120[2666], DS120[2667], DS120[2668], DS120[2669], DS120[2670], DS120[2671], DS120[2672]. # Note that there is no reversible (64,28,12) difference sets in # group [64,120]. ########################### ########################### ###########################