### 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 [64,104]. 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 [64,104].
    
    
# 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(64,104));' can be 
# used to create a list e of the elements of the group [64,104].
# In our list of (64,28,12) DSs in group [64,104], we have [1, 
# 2, 3, 4, 5, 6, 9, 11, 12, 13, 15, 17, 20, 25, 29, 
# 32, 37, 41, 46, 48, 49, 53, 54, 55, 56, 57, 61, 62].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[6], e[9], e[11], e[12], e[13], e[15], e[17], e[20], e[25], e[29], e[32], 
# e[37], e[41], e[46], e[48], e[49], e[53], e[54], e[55], e[56], e[57], e[61], e[62]]
# where e is the list of the elements of the group [64,104] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,104));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 104]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,104] is 616
### The list of all inequivalent (64,28,12) DSs in group [64,104] is 
  
  
DS104:=[ [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 15, 17, 20, 25, 29, 32, 37, 41, 46, 48, 49, 53, 54, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 15, 17, 20, 23, 29, 32, 37, 41, 43, 45, 49, 53, 54, 55, 56, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 16, 20, 23, 25, 27, 30, 31, 34, 35, 36, 39, 40, 41, 55, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 19, 20, 23, 25, 31, 34, 35, 37, 39, 43, 46, 50, 52, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 19, 20, 23, 25, 27, 30, 31, 34, 35, 37, 39, 55, 56, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 17, 20, 23, 29, 31, 32, 37, 41, 45, 46, 53, 54, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 20, 23, 25, 27, 30, 31, 35, 38, 39, 40, 41, 53, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 19, 20, 23, 25, 31, 38, 39, 43, 46, 50, 52, 53, 54, 55, 57 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 19, 20, 23, 25, 31, 33, 38, 39, 50, 52, 55, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 19, 20, 23, 25, 27, 30, 31, 38, 39, 53, 54, 55, 57, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 16, 17, 20, 23, 25, 31, 35, 38, 41, 50, 52, 53, 57, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 15, 16, 19, 20, 25, 28, 31, 33, 38, 39, 47, 49, 51, 52, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 13, 15, 16, 17, 20, 25, 28, 31, 35, 38, 41, 47, 49, 51, 52, 53, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 17, 20, 26, 32, 34, 36, 37, 38, 41, 44, 46, 54, 57, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 12, 13, 17, 20, 26, 28, 32, 34, 36, 37, 38, 41, 46, 49, 51, 54, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 19, 20, 27, 28, 29, 31, 33, 38, 39, 44, 47, 50, 53, 54, 56, 57, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 18, 19, 20, 27, 28, 29, 31, 33, 34, 38, 41, 44, 47, 50, 54, 55, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 15, 17, 18, 22, 27, 28, 29, 31, 35, 38, 41, 44, 47, 50, 53, 54, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 16, 25, 26, 27, 30, 31, 32, 33, 35, 36, 40, 41, 42, 48, 51, 54, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 16, 18, 19, 20, 28, 31, 33, 36, 41, 43, 45, 47, 49, 50, 51, 55, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 19, 22, 27, 29, 31, 33, 36, 41, 47, 49, 50, 51, 53, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 19, 22, 27, 28, 29, 31, 33, 36, 41, 44, 47, 50, 53, 57, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 19, 22, 24, 26, 27, 30, 31, 32, 41, 47, 51, 53, 54, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 19, 20, 28, 31, 33, 38, 39, 43, 45, 47, 49, 50, 51, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 19, 20, 27, 28, 29, 31, 33, 38, 39, 44, 47, 50, 55, 57, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 18, 24, 26, 27, 30, 31, 32, 35, 38, 39, 40, 42, 47, 51, 53, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 18, 19, 22, 24, 26, 27, 30, 31, 32, 39, 47, 51, 53, 54, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 17, 22, 27, 29, 31, 35, 36, 39, 47, 49, 50, 51, 55, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 17, 22, 27, 28, 29, 31, 35, 36, 39, 44, 47, 50, 55, 57, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 17, 20, 31, 35, 38, 41, 43, 44, 45, 47, 50, 53, 57, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 17, 20, 28, 31, 35, 38, 41, 43, 45, 47, 49, 50, 51, 53, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 15, 16, 17, 20, 27, 28, 29, 31, 35, 38, 41, 44, 47, 50, 53, 57, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 19, 20, 27, 28, 29, 31, 34, 35, 38, 39, 44, 47, 50, 55, 56, 57, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 18, 19, 22, 27, 29, 30, 31, 32, 35, 36, 39, 46, 47, 48, 50, 55, 56, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 18, 19, 22, 27, 28, 29, 31, 35, 36, 39, 44, 47, 50, 55, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 18, 19, 20, 27, 28, 29, 31, 35, 38, 41, 44, 47, 50, 53, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 18, 26, 27, 30, 31, 32, 34, 35, 37, 39, 40, 42, 46, 51, 55, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 16, 18, 25, 26, 27, 30, 31, 32, 35, 37, 39, 40, 42, 48, 51, 53, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 17, 20, 24, 26, 28, 29, 30, 33, 35, 36, 37, 38, 41, 47, 51, 52, 53, 55, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 20, 26, 29, 34, 36, 37, 38, 41, 43, 44, 54, 57, 58, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 20, 26, 28, 29, 34, 36, 37, 38, 41, 43, 49, 51, 54, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 20, 26, 27, 29, 34, 36, 37, 38, 41, 44, 49, 50, 54, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 20, 26, 27, 28, 29, 34, 36, 37, 38, 41, 50, 51, 54, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 17, 20, 24, 26, 28, 29, 30, 34, 36, 37, 38, 41, 47, 51, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 15, 26, 27, 28, 29, 33, 34, 36, 37, 40, 41, 42, 50, 51, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 15, 17, 26, 27, 29, 36, 37, 39, 41, 42, 44, 49, 50, 54, 55, 60, 62, 63 ], [ 1, 2, 3, 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38, 39, 42, 46, 49, 51, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 30, 33, 38, 40, 41, 46, 49, 52, 53, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 30, 33, 35, 38, 39, 41, 46, 49, 52, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 27, 35, 36, 38, 39, 41, 46, 49, 50, 53, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 27, 34, 35, 46, 49, 50, 53, 56, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 30, 34, 35, 38, 39, 40, 46, 49, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 22, 27, 35, 36, 38, 41, 42, 44, 49, 50, 53, 54, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 25, 28, 35, 37, 38, 40, 43, 51, 53, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 25, 30, 33, 36, 38, 40, 41, 49, 52, 54, 55, 56, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 26, 30, 32, 36, 40, 44, 47, 51, 57, 58, 59, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 28, 33, 37, 38, 39, 42, 44, 49, 51, 53, 54, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 27, 34, 37, 38, 39, 42, 44, 49, 50, 53, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 21, 28, 38, 40, 43, 46, 51, 53, 54, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 30, 33, 37, 38, 39, 41, 44, 49, 52, 53, 54, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 27, 36, 37, 38, 39, 41, 44, 49, 50, 53, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 32, 36, 37, 39, 40, 44, 51, 52, 53, 55, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 30, 34, 37, 38, 39, 40, 44, 49, 52, 53, 55, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 28, 36, 37, 38, 39, 40, 44, 49, 51, 53, 56, 59, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 28, 30, 32, 34, 37, 39, 40, 44, 53, 56, 59, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 25, 28, 35, 37, 38, 39, 42, 49, 51, 53, 54, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 25, 30, 37, 38, 40, 41, 49, 52, 53, 55, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 25, 30, 35, 37, 38, 39, 41, 49, 52, 53, 54, 59, 64 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 435
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS104[1], DS104[3], DS104[4], DS104[5], DS104[7], DS104[8], DS104[9], DS104[10], DS104[13], DS104[17], DS104[18], DS104[19], DS104[21], DS104[23], DS104[24], DS104[27], DS104[29], DS104[31], DS104[32], DS104[35], DS104[37], DS104[43], DS104[52], DS104[58], DS104[59], DS104[60], DS104[63], DS104[65], DS104[71], DS104[72], DS104[73], DS104[74], DS104[75], DS104[76], DS104[77], DS104[78], DS104[79], DS104[82], DS104[84], DS104[85], DS104[86], DS104[87], DS104[88], DS104[90], DS104[91], DS104[93], DS104[96], DS104[98], DS104[99], DS104[102], DS104[103], DS104[106], DS104[108], DS104[109], DS104[110], DS104[111], DS104[112], DS104[113], DS104[120], DS104[121], DS104[124], DS104[125], DS104[127], DS104[128], DS104[130], DS104[131], DS104[132], DS104[135], DS104[137], DS104[138], DS104[140], DS104[141], DS104[143], DS104[145], DS104[147], DS104[148], DS104[150], DS104[152], DS104[153], DS104[156], DS104[158], DS104[162], DS104[163], DS104[164], DS104[165], DS104[167], DS104[168], DS104[170], DS104[171], DS104[172], DS104[174], DS104[175], DS104[176], DS104[177], DS104[178], DS104[179], DS104[180], DS104[181], DS104[182], DS104[183], DS104[185], DS104[186], DS104[191], DS104[192], DS104[193], DS104[194], DS104[199], DS104[201], DS104[202], DS104[205], DS104[207], DS104[208], DS104[209], DS104[213], DS104[214], DS104[215], DS104[217], DS104[218], DS104[219], DS104[221], DS104[222], DS104[223], DS104[236], DS104[237], DS104[241], DS104[247], DS104[249], DS104[250], DS104[255], DS104[256], DS104[258], DS104[260], DS104[261], DS104[262], DS104[264], DS104[266], DS104[267], DS104[268], DS104[270], DS104[271], DS104[273], DS104[274], DS104[276], DS104[277], DS104[280], DS104[281], DS104[282], DS104[283], DS104[285], DS104[286], DS104[287], DS104[288], DS104[289], DS104[291], DS104[292], DS104[293], DS104[297], DS104[298], DS104[299], DS104[301], DS104[302], DS104[303], DS104[304], DS104[305], DS104[307], DS104[308], DS104[310], DS104[311], DS104[313], DS104[316], DS104[317], DS104[318], DS104[319], DS104[321], DS104[322], DS104[323], DS104[329], DS104[330], DS104[331], DS104[332], DS104[333], DS104[334], DS104[335], DS104[336], DS104[337], DS104[339], DS104[340], DS104[341], DS104[342], DS104[343], DS104[344], DS104[345], DS104[346], DS104[347], DS104[348], DS104[349], DS104[350], DS104[351], DS104[352], DS104[353], DS104[354], DS104[358], DS104[359], DS104[360], DS104[361], DS104[362], DS104[363], DS104[364], DS104[365], DS104[366], DS104[367], DS104[368], DS104[370], DS104[372], DS104[373], DS104[375], DS104[376], DS104[377], DS104[378], DS104[379], DS104[380], DS104[381], DS104[382], DS104[383], DS104[384], DS104[385], DS104[386], DS104[387], DS104[389], DS104[390], DS104[391], DS104[392], DS104[393], DS104[394], DS104[395], DS104[396], DS104[397], DS104[400], DS104[401], DS104[402], DS104[403], DS104[404], DS104[405], DS104[406], DS104[407], DS104[408], DS104[409], DS104[410], DS104[411], DS104[412], DS104[413], DS104[414], DS104[415], DS104[416], DS104[417], DS104[418], DS104[419], DS104[420], DS104[421], DS104[422], DS104[423], DS104[424], DS104[425], DS104[426], DS104[427], DS104[428], DS104[429], DS104[430], DS104[431], DS104[432], DS104[433], DS104[434], DS104[435], DS104[436], DS104[437], DS104[438], DS104[439], DS104[440], DS104[441], DS104[442], DS104[443], DS104[444], DS104[445], DS104[446], DS104[447], DS104[448], DS104[449], DS104[450], DS104[451], DS104[454], DS104[456], DS104[457], DS104[458], DS104[459], DS104[461], DS104[462], DS104[463], DS104[464], DS104[465], DS104[466], DS104[467], DS104[468], DS104[469], DS104[470], DS104[471], DS104[472], DS104[473], DS104[474], DS104[475], DS104[476], DS104[477], DS104[478], DS104[479], DS104[480], DS104[481], DS104[482], DS104[483], DS104[484], DS104[485], DS104[486], DS104[487], DS104[494], DS104[496], DS104[497], DS104[498], DS104[499], DS104[500], DS104[501], DS104[502], DS104[503], DS104[504], DS104[505], DS104[506], DS104[507], DS104[508], DS104[509], DS104[510], DS104[512], DS104[513], DS104[514], DS104[515], DS104[516], DS104[517], DS104[518], DS104[519], DS104[520], DS104[521], DS104[523], DS104[524], DS104[526], DS104[528], DS104[530], DS104[531], DS104[532], DS104[533], DS104[534], DS104[535], DS104[536], DS104[538], DS104[539], DS104[540], DS104[541], DS104[542], DS104[543], DS104[544], DS104[545], DS104[546], DS104[547], DS104[548], DS104[549], DS104[550], DS104[551], DS104[552], DS104[553], DS104[554], DS104[555], DS104[556], DS104[558], DS104[559], DS104[560], DS104[561], DS104[562], DS104[563], DS104[564], DS104[565], DS104[566], DS104[567], DS104[568], DS104[569], DS104[570], DS104[571], DS104[572], DS104[573], DS104[575], DS104[576], DS104[577], DS104[578], DS104[579], DS104[580], DS104[581], DS104[582], DS104[583], DS104[584], DS104[585], DS104[586], DS104[587], DS104[588], DS104[589], DS104[590], DS104[591], DS104[592], DS104[593], DS104[594], DS104[595], DS104[596], DS104[597], DS104[598], DS104[599], DS104[600], DS104[601], DS104[602], DS104[603], DS104[604], DS104[605], DS104[606], DS104[607], DS104[608], DS104[609], DS104[610], DS104[611], DS104[612], DS104[613], DS104[614], DS104[615], DS104[616]. 
         
         
  
# Finally, We list all inequivalent reversible (64,28,12) difference 
# sets in group [64,104].
  
  
### The number of inequivalent reversible (64,28,12) DSs in group [64,104] is 16
### The list of all inequivalent reversible (64,28,12) DSs in group [64,104] is 
  
  
RDS104:=[ [ 2, 4, 5, 8, 9, 10, 13, 19, 20, 21, 27, 28, 32, 33, 35, 39, 42, 43, 45, 46, 47, 48, 49, 52, 54, 57, 58, 60 ], [ 2, 4, 5, 8, 9, 10, 13, 19, 20, 21, 23, 27, 28, 32, 33, 35, 39, 42, 44, 46, 47, 48, 49, 52, 54, 57, 59, 64 ], [ 2, 4, 5, 6, 8, 9, 10, 13, 18, 19, 21, 22, 27, 28, 32, 33, 35, 41, 43, 45, 46, 47, 48, 49, 52, 54, 58, 60 ], [ 2, 4, 5, 6, 8, 9, 10, 13, 18, 19, 21, 22, 23, 27, 28, 32, 33, 35, 41, 44, 46, 47, 48, 49, 52, 54, 59, 64 ], [ 2, 3, 4, 5, 8, 9, 10, 14, 16, 19, 20, 21, 27, 28, 32, 37, 39, 42, 43, 45, 46, 47, 48, 49, 52, 57, 58, 60 ], [ 2, 3, 4, 5, 8, 9, 10, 14, 16, 19, 20, 21, 23, 27, 28, 32, 37, 39, 42, 44, 46, 47, 48, 49, 52, 57, 59, 64 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 19, 21, 22, 27, 28, 32, 37, 41, 43, 45, 46, 47, 48, 49, 52, 58, 60 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 19, 21, 22, 23, 27, 28, 32, 37, 41, 44, 46, 47, 48, 49, 52, 59, 64 ], [ 1, 2, 4, 7, 8, 9, 10, 13, 18, 19, 20, 27, 28, 32, 33, 35, 41, 42, 43, 45, 46, 47, 48, 49, 52, 54, 58, 60 ], [ 1, 2, 4, 7, 8, 9, 10, 13, 18, 19, 20, 23, 27, 28, 32, 33, 35, 41, 42, 44, 46, 47, 48, 49, 52, 54, 59, 64 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 13, 19, 22, 27, 28, 32, 33, 35, 39, 43, 45, 46, 47, 48, 49, 52, 54, 57, 58, 60 ], [ 1, 2, 4, 6, 7, 8, 9, 10, 13, 19, 22, 23, 27, 28, 32, 33, 35, 39, 44, 46, 47, 48, 49, 52, 54, 57, 59, 64 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 14, 16, 18, 19, 20, 27, 28, 32, 37, 41, 42, 43, 45, 46, 47, 48, 49, 52, 58, 60 ], [ 1, 2, 3, 4, 7, 8, 9, 10, 14, 16, 18, 19, 20, 23, 27, 28, 32, 37, 41, 42, 44, 46, 47, 48, 49, 52, 59, 64 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 10, 14, 16, 19, 22, 27, 28, 32, 37, 39, 43, 45, 46, 47, 48, 49, 52, 57, 58, 60 ], [ 1, 2, 3, 4, 6, 7, 8, 9, 10, 14, 16, 19, 22, 23, 27, 28, 32, 37, 39, 44, 46, 47, 48, 49, 52, 57, 59, 64 ] ];
  
  
  
   
   
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