### 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 [64,133]. 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 [64,133].
    
    
# 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(64,133));' can be 
# used to create a list e of the elements of the group [64,133].
# In our list of (64,28,12) DSs in group [64,133], we have [1, 
# 2, 3, 4, 5, 9, 10, 11, 14, 16, 19, 22, 23, 27, 30, 
# 33, 37, 39, 42, 43, 44, 51, 53, 54, 57, 58, 62, 63].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[9], e[10], e[11], e[14], e[16], e[19], e[22], e[23], e[27], e[30], e[33], 
# e[37], e[39], e[42], e[43], e[44], e[51], e[53], e[54], e[57], e[58], e[62], e[63]]
# where e is the list of the elements of the group [64,133] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,133));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 133]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,133] is 2512
### The list of all inequivalent (64,28,12) DSs in group [64,133] is 
  
  
DS133:=[ [ 1, 2, 3, 4, 5, 9, 10, 11, 14, 16, 19, 22, 23, 27, 30, 33, 37, 39, 42, 43, 44, 51, 53, 54, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 13, 14, 16, 19, 22, 28, 29, 30, 33, 37, 39, 42, 45, 51, 55, 57, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 13, 14, 16, 19, 22, 28, 29, 30, 33, 37, 39, 42, 43, 45, 51, 55, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 13, 14, 16, 19, 22, 23, 30, 34, 35, 37, 39, 42, 43, 44, 49, 50, 51, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 13, 14, 16, 19, 22, 23, 28, 29, 30, 33, 37, 39, 42, 44, 51, 55, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 9, 10, 11, 13, 14, 16, 19, 22, 23, 28, 29, 30, 33, 37, 39, 42, 43, 44, 51, 55, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 19, 22, 23, 26, 31, 33, 38, 40, 42, 44, 46, 52, 55, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 19, 22, 23, 26, 31, 33, 38, 40, 42, 43, 44, 46, 52, 55, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 19, 22, 23, 26, 31, 33, 38, 40, 42, 43, 44, 46, 52, 53, 55, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 16, 17, 19, 22, 25, 26, 30, 33, 36, 40, 42, 45, 48, 55, 56, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 16, 17, 19, 22, 25, 26, 30, 33, 36, 40, 42, 43, 45, 48, 55, 56, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 16, 17, 19, 22, 23, 25, 26, 30, 33, 36, 40, 42, 44, 48, 55, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 16, 17, 19, 22, 23, 25, 26, 30, 33, 36, 40, 42, 43, 44, 48, 55, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 15, 16, 17, 19, 22, 23, 26, 30, 33, 38, 40, 42, 44, 46, 55, 59, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 8, 10, 11, 13, 15, 16, 17, 19, 22, 23, 26, 30, 33, 38, 40, 42, 43, 44, 46, 55, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 24, 25, 28, 30, 31, 32, 33, 35, 38, 39, 42, 46, 50, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 24, 25, 27, 28, 30, 31, 32, 33, 35, 38, 39, 42, 46, 49, 54, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 15, 18, 22, 23, 25, 26, 27, 30, 36, 40, 42, 43, 45, 48, 51, 52, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 15, 17, 18, 22, 23, 25, 26, 27, 30, 36, 39, 42, 43, 45, 48, 51, 52, 59, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 15, 16, 17, 22, 24, 25, 28, 30, 33, 35, 38, 41, 42, 46, 50, 52, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 15, 16, 17, 22, 24, 25, 27, 28, 30, 33, 35, 38, 41, 42, 46, 49, 52, 54, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 15, 18, 22, 23, 26, 27, 32, 37, 40, 42, 43, 45, 46, 51, 56, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 15, 17, 18, 22, 23, 26, 27, 32, 37, 39, 42, 43, 45, 46, 51, 56, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 18, 22, 23, 26, 27, 32, 36, 40, 42, 43, 45, 46, 51, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 14, 15, 17, 18, 22, 23, 26, 27, 32, 36, 39, 42, 43, 45, 46, 51, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 16, 17, 22, 24, 25, 28, 32, 33, 35, 36, 41, 42, 46, 50, 54, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 16, 17, 22, 24, 25, 27, 28, 32, 33, 35, 36, 41, 42, 46, 49, 54, 56, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 25, 28, 32, 33, 35, 36, 41, 42, 47, 50, 52, 54, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 25, 27, 28, 32, 33, 35, 36, 41, 42, 47, 49, 52, 54, 56, 61 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 24, 25, 28, 32, 33, 35, 36, 41, 42, 46, 50, 52, 54, 56, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 24, 25, 27, 28, 32, 33, 35, 36, 41, 42, 46, 49, 52, 54, 56 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 15, 16, 19, 22, 24, 25, 28, 32, 33, 35, 38, 39, 42, 46, 50, 52, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 15, 16, 19, 22, 24, 25, 27, 28, 32, 33, 35, 38, 39, 42, 46, 49, 52, 54, 57 ], [ 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 16, 17, 21, 23, 31, 35, 38, 41, 43, 44, 49, 50, 51, 52, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 16, 17, 21, 23, 27, 31, 35, 38, 41, 43, 44, 51, 52, 53, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 16, 17, 21, 23, 30, 33, 36, 41, 43, 44, 49, 50, 51, 53, 54, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 16, 17, 21, 23, 27, 30, 33, 36, 41, 43, 44, 51, 53, 54, 56, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 14, 17, 21, 23, 29, 30, 33, 38, 41, 44, 49, 53, 54, 56, 57, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 14, 17, 21, 23, 29, 30, 33, 38, 41, 43, 44, 49, 53, 54, 56, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 19, 21, 23, 28, 29, 30, 36, 37, 38, 39, 43, 44, 51, 53, 54, 55, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 17, 21, 28, 29, 30, 35, 36, 37, 38, 41, 45, 51, 53, 57, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 17, 21, 28, 29, 30, 35, 36, 37, 38, 41, 43, 45, 51, 53, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 17, 21, 23, 28, 29, 30, 35, 36, 37, 38, 41, 44, 51, 53, 57, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 17, 21, 23, 28, 29, 30, 35, 36, 37, 38, 41, 43, 44, 51, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 21, 23, 30, 34, 35, 36, 41, 43, 44, 49, 50, 51, 55, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 21, 23, 27, 30, 34, 35, 36, 41, 43, 44, 51, 55, 56, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 21, 23, 30, 35, 38, 41, 43, 44, 49, 50, 51, 53, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 21, 23, 27, 30, 35, 38, 41, 43, 44, 51, 53, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 19, 21, 23, 28, 29, 30, 33, 38, 39, 43, 44, 51, 55, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 18, 19, 21, 23, 29, 30, 33, 38, 41, 44, 49, 55, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 18, 19, 21, 23, 29, 30, 33, 38, 41, 43, 44, 49, 55, 56, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 17, 21, 28, 29, 30, 35, 38, 41, 45, 51, 53, 56, 57, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 17, 21, 28, 29, 30, 35, 38, 41, 43, 45, 51, 53, 56, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 17, 21, 23, 29, 30, 34, 35, 38, 41, 44, 49, 55, 56, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 17, 21, 23, 29, 30, 34, 35, 38, 41, 43, 44, 49, 55, 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### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 992
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS133[1], DS133[16], DS133[18], DS133[20], DS133[27], DS133[30], DS133[36], DS133[38], DS133[39], DS133[43], DS133[44], DS133[45], DS133[50], DS133[51], DS133[59], DS133[62], DS133[64], DS133[65], DS133[81], DS133[83], DS133[87], DS133[92], DS133[98], DS133[100], DS133[102], DS133[107], DS133[112], DS133[113], DS133[114], DS133[118], DS133[126], DS133[127], DS133[128], DS133[132], DS133[134], DS133[140], DS133[142], DS133[143], DS133[144], DS133[145], DS133[148], DS133[153], DS133[156], DS133[158], DS133[159], DS133[160], DS133[165], DS133[167], DS133[173], DS133[176], DS133[177], DS133[187], DS133[188], DS133[190], DS133[196], DS133[197], DS133[198], DS133[199], DS133[201], DS133[202], DS133[209], DS133[220], DS133[223], DS133[226], DS133[234], DS133[238], DS133[240], DS133[241], DS133[243], DS133[245], DS133[257], DS133[258], DS133[260], DS133[271], DS133[272], DS133[283], DS133[288], DS133[291], DS133[293], DS133[298], DS133[303], DS133[307], DS133[312], DS133[313], DS133[315], DS133[318], DS133[321], DS133[326], DS133[328], DS133[329], DS133[331], DS133[332], DS133[333], DS133[334], DS133[337], DS133[342], DS133[343], DS133[344], DS133[348], DS133[352], DS133[361], DS133[366], DS133[369], DS133[383], DS133[384], DS133[385], DS133[396], DS133[399], DS133[402], DS133[403], DS133[404], DS133[409], DS133[414], DS133[415], DS133[416], DS133[417], DS133[420], DS133[421], DS133[423], DS133[424], DS133[428], DS133[429], DS133[433], DS133[434], DS133[452], DS133[454], DS133[458], DS133[468], DS133[469], DS133[484], DS133[486], DS133[487], DS133[488], DS133[489], DS133[490], DS133[491], DS133[494], DS133[499], DS133[505], DS133[514], DS133[520], DS133[521], DS133[522], DS133[524], DS133[532], DS133[534], DS133[535], DS133[536], DS133[544], DS133[546], DS133[549], DS133[554], DS133[558], DS133[561], DS133[564], DS133[574], DS133[575], DS133[583], DS133[584], DS133[588], DS133[593], DS133[602], DS133[606], DS133[609], DS133[617], DS133[622], DS133[624], DS133[627], DS133[628], DS133[631], DS133[634], DS133[641], DS133[644], DS133[654], DS133[656], DS133[662], DS133[664], DS133[665], DS133[666], DS133[667], DS133[674], DS133[675], DS133[678], DS133[679], DS133[680], DS133[681], DS133[682], DS133[683], DS133[685], DS133[687], DS133[688], DS133[695], DS133[696], DS133[702], DS133[705], DS133[706], DS133[709], DS133[710], DS133[716], DS133[717], DS133[718], DS133[719], DS133[723], DS133[726], DS133[728], DS133[731], DS133[732], DS133[734], DS133[735], DS133[745], DS133[759], DS133[761], DS133[767], DS133[768], DS133[769], DS133[774], DS133[775], DS133[777], DS133[778], DS133[785], DS133[787], DS133[791], DS133[795], DS133[796], DS133[797], DS133[798], DS133[799], DS133[800], DS133[801], DS133[803], DS133[805], DS133[807], DS133[808], DS133[816], DS133[819], DS133[825], DS133[826], DS133[830], DS133[833], DS133[834], DS133[837], DS133[839], DS133[847], DS133[849], DS133[851], DS133[852], DS133[855], DS133[856], DS133[858], DS133[860], DS133[861], DS133[865], DS133[867], DS133[870], DS133[872], DS133[873], DS133[874], DS133[879], DS133[880], DS133[881], DS133[883], DS133[885], DS133[890], DS133[891], DS133[896], DS133[897], DS133[898], DS133[899], DS133[900], DS133[901], DS133[903], DS133[906], DS133[915], DS133[919], DS133[921], DS133[927], DS133[929], DS133[935], DS133[936], DS133[937], DS133[938], DS133[947], DS133[954], DS133[960], DS133[961], DS133[962], DS133[963], DS133[964], DS133[965], DS133[969], DS133[970], DS133[972], DS133[976], DS133[977], DS133[980], DS133[981], DS133[982], DS133[983], DS133[986], DS133[987], DS133[991], DS133[992], DS133[993], DS133[995], DS133[998], DS133[1014], DS133[1017], DS133[1018], DS133[1019], DS133[1020], DS133[1021], DS133[1022], DS133[1027], DS133[1041], DS133[1047], DS133[1053], DS133[1058], DS133[1078], DS133[1079], DS133[1087], DS133[1090], DS133[1095], DS133[1096], DS133[1097], DS133[1098], DS133[1100], DS133[1103], DS133[1110], DS133[1112], DS133[1121], DS133[1131], DS133[1135], DS133[1137], DS133[1139], DS133[1140], DS133[1141], DS133[1142], DS133[1152], DS133[1155], DS133[1158], DS133[1173], DS133[1187], DS133[1188], DS133[1190], DS133[1200], DS133[1202], DS133[1204], DS133[1231], DS133[1232], DS133[1239], DS133[1248], DS133[1249], DS133[1250], DS133[1251], DS133[1252], DS133[1256], DS133[1268], DS133[1269], DS133[1277], DS133[1278], DS133[1287], DS133[1288], DS133[1290], DS133[1292], DS133[1293], DS133[1294], DS133[1296], DS133[1297], DS133[1298], DS133[1301], DS133[1316], DS133[1317], DS133[1318], DS133[1319], DS133[1320], DS133[1321], DS133[1322], DS133[1323], DS133[1325], DS133[1326], DS133[1327], DS133[1328], DS133[1330], DS133[1333], DS133[1334], DS133[1335], DS133[1336], DS133[1337], DS133[1338], DS133[1341], DS133[1342], DS133[1343], DS133[1344], DS133[1345], DS133[1346], DS133[1347], DS133[1348], DS133[1349], DS133[1351], DS133[1354], DS133[1358], DS133[1363], DS133[1364], DS133[1366], DS133[1372], DS133[1377], DS133[1378], DS133[1385], DS133[1390], DS133[1391], DS133[1392], DS133[1413], DS133[1414], DS133[1415], DS133[1423], DS133[1427], DS133[1435], DS133[1436], DS133[1441], DS133[1458], DS133[1463], DS133[1465], DS133[1466], DS133[1468], DS133[1473], DS133[1474], DS133[1475], DS133[1485], DS133[1487], DS133[1490], DS133[1491], DS133[1492], DS133[1493], DS133[1494], DS133[1495], DS133[1496], DS133[1497], DS133[1498], DS133[1499], DS133[1505], DS133[1506], DS133[1508], DS133[1509], DS133[1510], DS133[1511], DS133[1516], DS133[1521], DS133[1522], DS133[1523], DS133[1524], DS133[1525], DS133[1527], DS133[1529], DS133[1532], DS133[1539], DS133[1543], DS133[1545], DS133[1548], DS133[1554], DS133[1556], DS133[1561], DS133[1562], DS133[1573], DS133[1577], DS133[1581], DS133[1582], DS133[1583], DS133[1584], DS133[1588], DS133[1592], DS133[1594], DS133[1598], DS133[1602], DS133[1603], DS133[1604], DS133[1605], DS133[1606], DS133[1608], DS133[1609], DS133[1623], DS133[1625], DS133[1627], DS133[1629], DS133[1631], DS133[1632], DS133[1633], DS133[1634], DS133[1635], DS133[1639], DS133[1641], DS133[1642], DS133[1644], DS133[1645], DS133[1646], DS133[1648], DS133[1649], DS133[1651], DS133[1654], DS133[1655], DS133[1656], DS133[1657], DS133[1662], DS133[1674], DS133[1677], DS133[1679], DS133[1680], DS133[1684], DS133[1685], DS133[1686], DS133[1689], DS133[1690], DS133[1691], DS133[1706], DS133[1707], DS133[1711], DS133[1712], DS133[1714], DS133[1729], DS133[1737], DS133[1738], DS133[1743], DS133[1755], DS133[1760], DS133[1761], DS133[1766], DS133[1768], DS133[1769], DS133[1771], DS133[1772], DS133[1773], DS133[1774], DS133[1776], DS133[1777], DS133[1778], DS133[1783], DS133[1789], DS133[1790], DS133[1791], DS133[1792], DS133[1793], DS133[1794], DS133[1802], DS133[1803], DS133[1804], DS133[1808], DS133[1809], DS133[1816], DS133[1818], DS133[1819], DS133[1824], DS133[1825], DS133[1827], DS133[1828], DS133[1829], DS133[1831], DS133[1833], DS133[1834], DS133[1835], DS133[1836], DS133[1842], DS133[1844], DS133[1850], DS133[1851], DS133[1852], DS133[1853], DS133[1854], DS133[1855], DS133[1860], DS133[1864], DS133[1869], DS133[1870], DS133[1873], DS133[1875], DS133[1876], DS133[1878], DS133[1879], DS133[1880], DS133[1885], DS133[1886], DS133[1894], DS133[1895], DS133[1896], DS133[1897], DS133[1898], DS133[1900], DS133[1904], DS133[1905], DS133[1913], DS133[1915], DS133[1916], DS133[1917], DS133[1918], DS133[1919], DS133[1927], DS133[1928], DS133[1929], DS133[1930], DS133[1932], DS133[1935], DS133[1943], DS133[1945], DS133[1946], DS133[1949], DS133[1951], DS133[1952], DS133[1953], DS133[1954], DS133[1956], DS133[1957], DS133[1958], DS133[1959], DS133[1962], DS133[1964], DS133[1966], DS133[1968], DS133[1969], DS133[1970], DS133[1971], DS133[1972], DS133[1973], DS133[1974], DS133[1976], DS133[1977], DS133[1978], DS133[1983], DS133[1985], DS133[1986], DS133[1991], DS133[1992], DS133[1993], DS133[1995], DS133[1996], DS133[1999], DS133[2000], DS133[2001], DS133[2002], DS133[2003], DS133[2020], DS133[2024], DS133[2027], DS133[2032], DS133[2034], DS133[2038], DS133[2053], DS133[2054], DS133[2055], DS133[2059], DS133[2062], DS133[2068], DS133[2069], DS133[2073], DS133[2084], DS133[2088], DS133[2091], DS133[2092], DS133[2093], DS133[2094], DS133[2096], DS133[2097], DS133[2098], DS133[2099], DS133[2100], DS133[2101], DS133[2102], DS133[2103], DS133[2104], DS133[2105], DS133[2106], DS133[2109], DS133[2110], DS133[2111], DS133[2112], DS133[2113], DS133[2114], DS133[2115], DS133[2116], DS133[2119], DS133[2120], DS133[2121], DS133[2122], DS133[2123], DS133[2124], DS133[2125], DS133[2127], DS133[2128], DS133[2130], DS133[2131], DS133[2132], DS133[2134], DS133[2135], DS133[2145], DS133[2148], DS133[2152], DS133[2153], DS133[2154], DS133[2155], DS133[2156], DS133[2157], DS133[2158], DS133[2159], DS133[2160], DS133[2161], DS133[2162], DS133[2163], DS133[2164], DS133[2165], DS133[2166], DS133[2167], DS133[2168], DS133[2169], DS133[2170], DS133[2171], DS133[2172], DS133[2173], DS133[2174], DS133[2175], DS133[2176], DS133[2177], DS133[2178], DS133[2179], DS133[2180], DS133[2181], DS133[2182], DS133[2183], DS133[2184], DS133[2185], DS133[2186], DS133[2187], DS133[2188], DS133[2189], DS133[2190], DS133[2191], DS133[2192], DS133[2193], DS133[2194], DS133[2195], DS133[2196], DS133[2197], DS133[2198], DS133[2199], DS133[2200], DS133[2201], DS133[2202], DS133[2203], DS133[2204], DS133[2205], DS133[2206], DS133[2207], DS133[2208], DS133[2209], DS133[2210], DS133[2211], DS133[2212], DS133[2213], DS133[2215], DS133[2216], DS133[2217], DS133[2218], DS133[2234], DS133[2237], DS133[2238], DS133[2243], DS133[2244], DS133[2245], DS133[2246], DS133[2247], DS133[2248], DS133[2249], DS133[2250], DS133[2251], DS133[2252], DS133[2253], DS133[2254], DS133[2255], DS133[2256], DS133[2257], DS133[2258], DS133[2259], DS133[2260], DS133[2261], DS133[2262], DS133[2263], DS133[2265], DS133[2268], DS133[2269], DS133[2270], DS133[2272], DS133[2273], DS133[2274], DS133[2277], DS133[2278], DS133[2279], DS133[2280], DS133[2281], DS133[2282], DS133[2283], DS133[2284], DS133[2285], DS133[2286], DS133[2287], DS133[2288], DS133[2289], DS133[2290], DS133[2292], DS133[2293], DS133[2294], DS133[2295], DS133[2296], DS133[2297], DS133[2298], DS133[2299], DS133[2301], DS133[2302], DS133[2303], DS133[2304], DS133[2305], DS133[2306], DS133[2307], DS133[2308], DS133[2310], DS133[2311], DS133[2312], DS133[2313], DS133[2314], DS133[2315], DS133[2317], DS133[2318], DS133[2319], DS133[2320], DS133[2321], DS133[2322], DS133[2323], DS133[2325], DS133[2326], DS133[2327], DS133[2328], DS133[2329], DS133[2330], DS133[2333], DS133[2335], DS133[2337], DS133[2338], DS133[2339], DS133[2340], DS133[2341], DS133[2342], DS133[2343], DS133[2344], DS133[2345], DS133[2346], DS133[2347], DS133[2348], DS133[2349], DS133[2350], DS133[2351], DS133[2352], DS133[2353], DS133[2354], DS133[2355], DS133[2356], DS133[2357], DS133[2358], DS133[2359], DS133[2360], DS133[2361], DS133[2362], DS133[2363], DS133[2364], DS133[2365], DS133[2366], DS133[2367], DS133[2368], DS133[2369], DS133[2370], DS133[2371], DS133[2372], DS133[2373], DS133[2374], DS133[2379], DS133[2383], DS133[2389], DS133[2399], DS133[2400], DS133[2401], DS133[2402], DS133[2403], DS133[2404], DS133[2405], DS133[2406], DS133[2407], DS133[2408], DS133[2409], DS133[2410], DS133[2411], DS133[2412], DS133[2413], DS133[2414], DS133[2415], DS133[2416], DS133[2417], DS133[2418], DS133[2419], DS133[2420], DS133[2421], DS133[2422], DS133[2423], DS133[2424], DS133[2425], DS133[2426], DS133[2427], DS133[2428], DS133[2429], DS133[2430], DS133[2431], DS133[2432], DS133[2433], DS133[2434], DS133[2435], DS133[2436], DS133[2437], DS133[2438], DS133[2439], DS133[2440], DS133[2441], DS133[2442], DS133[2443], DS133[2444], DS133[2445], DS133[2446], DS133[2447], DS133[2448], DS133[2449], DS133[2450], DS133[2451], DS133[2452], DS133[2453], DS133[2454], DS133[2455], DS133[2456], DS133[2457], DS133[2458], DS133[2459], DS133[2460], DS133[2461], DS133[2462], DS133[2463], DS133[2464], DS133[2465], DS133[2467], DS133[2469], DS133[2470], DS133[2471], DS133[2472], DS133[2473], DS133[2474], DS133[2475], DS133[2476], DS133[2477], DS133[2478], DS133[2479], DS133[2480], DS133[2481], DS133[2482], DS133[2483], DS133[2484], DS133[2485], DS133[2486], DS133[2487], DS133[2488], DS133[2489], DS133[2490], DS133[2491], DS133[2493], DS133[2494], DS133[2495], DS133[2496], DS133[2497], DS133[2498], DS133[2499], DS133[2500], DS133[2501], DS133[2502], DS133[2503], DS133[2504], DS133[2505], DS133[2506], DS133[2507], DS133[2508], DS133[2509], DS133[2510], DS133[2511], DS133[2512]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,133].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,133] is 80
### The list of all inequivalent reversible (64,28,12) DSs in group [64,133] is 
  
  
RDS133:=[ [ 3, 6, 8, 9, 13, 14, 17, 20, 22, 23, 25, 27, 28, 35, 38, 39, 40, 42, 47, 49, 53, 56, 57, 58, 59, 60, 61, 63 ], [ 3, 5, 6, 8, 9, 13, 14, 17, 21, 22, 23, 25, 27, 28, 33, 35, 38, 39, 40, 47, 49, 54, 56, 57, 58, 59, 60, 61 ], [ 3, 4, 6, 8, 9, 13, 14, 19, 20, 22, 23, 25, 28, 34, 35, 38, 39, 42, 47, 50, 55, 56, 57, 58, 59, 60, 61, 62 ], [ 3, 4, 6, 8, 9, 13, 14, 19, 20, 22, 23, 25, 27, 28, 34, 35, 38, 39, 42, 47, 49, 55, 56, 57, 58, 59, 60, 61 ], [ 3, 4, 6, 8, 9, 13, 14, 18, 19, 20, 22, 23, 25, 27, 28, 35, 38, 41, 42, 47, 49, 53, 56, 58, 59, 60, 61, 63 ], [ 3, 4, 5, 8, 9, 13, 14, 19, 20, 21, 23, 25, 27, 28, 33, 35, 38, 39, 42, 47, 49, 54, 56, 57, 58, 59, 60, 61 ], [ 3, 4, 5, 8, 9, 13, 14, 17, 19, 20, 21, 23, 25, 27, 28, 35, 38, 40, 42, 47, 49, 53, 56, 58, 59, 60, 61, 63 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 18, 19, 21, 22, 23, 25, 27, 28, 33, 35, 38, 41, 47, 49, 54, 56, 58, 59, 60, 61 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 17, 19, 21, 22, 23, 25, 28, 34, 35, 38, 40, 47, 50, 55, 56, 58, 59, 60, 61, 62 ], [ 3, 4, 5, 6, 8, 9, 13, 14, 17, 19, 21, 22, 23, 25, 27, 28, 34, 35, 38, 40, 47, 49, 55, 56, 58, 59, 60, 61 ], [ 2, 3, 8, 9, 12, 13, 14, 17, 23, 25, 27, 28, 30, 33, 35, 38, 39, 40, 47, 49, 52, 54, 56, 57, 58, 59, 60, 61 ], [ 2, 3, 8, 9, 10, 12, 13, 14, 17, 23, 25, 27, 28, 31, 35, 38, 39, 40, 47, 49, 53, 56, 57, 58, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 12, 14, 17, 20, 22, 23, 25, 27, 28, 30, 38, 39, 40, 42, 47, 49, 52, 56, 57, 58, 59, 60, 61 ], [ 2, 3, 6, 8, 9, 12, 13, 14, 20, 22, 23, 25, 28, 30, 34, 35, 38, 42, 47, 50, 52, 55, 56, 58, 59, 60, 61, 62 ], [ 2, 3, 6, 8, 9, 12, 13, 14, 20, 22, 23, 25, 27, 28, 30, 34, 35, 38, 42, 47, 49, 52, 55, 56, 58, 59, 60, 61 ], [ 2, 3, 6, 8, 9, 11, 12, 13, 20, 22, 23, 25, 27, 28, 32, 35, 36, 37, 38, 42, 47, 49, 53, 58, 59, 60, 61, 63 ], [ 2, 3, 6, 8, 9, 11, 12, 13, 14, 20, 22, 23, 25, 27, 28, 32, 35, 38, 42, 47, 49, 53, 56, 58, 59, 60, 61, 63 ], [ 2, 3, 5, 8, 9, 12, 13, 14, 20, 21, 23, 25, 27, 28, 30, 33, 35, 38, 42, 47, 49, 52, 54, 56, 58, 59, 60, 61 ], [ 2, 3, 5, 8, 9, 10, 12, 13, 14, 20, 21, 23, 25, 27, 28, 31, 35, 38, 42, 47, 49, 53, 56, 58, 59, 60, 61, 63 ], [ 2, 3, 5, 6, 8, 9, 11, 12, 13, 21, 22, 23, 25, 27, 28, 32, 33, 35, 36, 37, 38, 47, 49, 54, 58, 59, 60, 61 ], [ 2, 3, 5, 6, 8, 9, 11, 12, 13, 14, 21, 22, 23, 25, 27, 28, 32, 33, 35, 38, 47, 49, 54, 56, 58, 59, 60, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 12, 14, 17, 21, 22, 23, 25, 27, 28, 31, 38, 39, 40, 47, 49, 56, 57, 58, 59, 60, 61 ], [ 2, 3, 5, 6, 8, 9, 10, 12, 13, 14, 21, 22, 23, 25, 28, 31, 34, 35, 38, 47, 50, 55, 56, 58, 59, 60, 61, 62 ], [ 2, 3, 5, 6, 8, 9, 10, 12, 13, 14, 21, 22, 23, 25, 27, 28, 31, 34, 35, 38, 47, 49, 55, 56, 58, 59, 60, 61 ], [ 2, 3, 4, 8, 9, 12, 13, 14, 18, 19, 23, 25, 27, 28, 30, 33, 35, 38, 41, 47, 49, 52, 54, 56, 58, 59, 60, 61 ], [ 2, 3, 4, 8, 9, 12, 13, 14, 17, 19, 25, 28, 30, 34, 35, 38, 40, 43, 44, 45, 47, 50, 52, 55, 56, 61, 62, 64 ], [ 2, 3, 4, 8, 9, 12, 13, 14, 17, 19, 25, 27, 28, 30, 34, 35, 38, 40, 43, 44, 45, 47, 49, 52, 55, 56, 61, 64 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