### 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 [64,158]. 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 [64,158].
    
    
# 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(64,158));' can be 
# used to create a list e of the elements of the group [64,158].
# In our list of (64,28,12) DSs in group [64,158], we have [1, 
# 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 28, 
# 29, 30, 34, 36, 40, 43, 51, 54, 56, 57, 60, 63, 64].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[7], e[9], e[10], e[11], e[13], e[16], e[18], e[21], e[23], e[28], e[29], 
# e[30], e[34], e[36], e[40], e[43], e[51], e[54], e[56], e[57], e[60], e[63], e[64]]
# where e is the list of the elements of the group [64,158] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,158));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 158]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,158] is 1778
### The list of all inequivalent (64,28,12) DSs in group [64,158] is 
  
  
DS158:=[ [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 28, 29, 30, 34, 36, 40, 43, 51, 54, 56, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 18, 21, 23, 28, 29, 30, 34, 36, 40, 43, 44, 51, 54, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 19, 21, 23, 28, 29, 30, 37, 39, 43, 51, 53, 54, 55, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 19, 21, 23, 28, 29, 30, 37, 39, 43, 44, 51, 53, 54, 55, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 19, 21, 23, 28, 29, 30, 34, 37, 39, 43, 51, 54, 56, 57, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 19, 21, 23, 28, 29, 30, 34, 37, 39, 43, 44, 51, 54, 56, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 18, 19, 21, 23, 29, 30, 37, 41, 43, 49, 53, 54, 55, 56, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 18, 19, 21, 23, 29, 30, 37, 41, 43, 44, 49, 53, 54, 55, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 18, 19, 21, 23, 29, 30, 34, 37, 41, 43, 49, 54, 56, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 18, 19, 21, 23, 29, 30, 34, 37, 41, 43, 44, 49, 54, 56, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 29, 30, 34, 38, 40, 43, 49, 54, 57, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 21, 23, 29, 30, 34, 38, 40, 43, 44, 49, 54, 57, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 18, 19, 21, 24, 25, 27, 30, 37, 41, 46, 51, 52, 53, 54, 55, 56, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 18, 19, 21, 24, 25, 27, 30, 34, 37, 41, 46, 51, 52, 54, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 18, 19, 21, 24, 25, 27, 28, 30, 37, 41, 46, 49, 52, 53, 54, 55, 56 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 18, 19, 21, 24, 25, 27, 28, 30, 34, 37, 41, 46, 49, 52, 54, 56, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 16, 18, 21, 24, 25, 27, 30, 34, 38, 40, 46, 51, 52, 54, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 16, 18, 21, 24, 25, 27, 28, 30, 34, 38, 40, 46, 49, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 21, 23, 26, 31, 36, 41, 44, 45, 46, 49, 50, 51, 52, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 21, 23, 26, 28, 31, 36, 41, 44, 45, 46, 50, 52, 57, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 21, 23, 25, 28, 29, 31, 36, 41, 45, 47, 51, 52, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 18, 21, 23, 26, 31, 36, 39, 44, 45, 46, 49, 50, 51, 52, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 18, 21, 23, 26, 28, 31, 36, 39, 44, 45, 46, 50, 52, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 18, 21, 23, 25, 28, 29, 31, 36, 39, 45, 47, 51, 52, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 21, 25, 26, 28, 29, 36, 41, 43, 44, 52, 57, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 21, 23, 25, 26, 28, 36, 41, 50, 51, 52, 57, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 25, 26, 28, 29, 36, 39, 43, 44, 52, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 23, 29, 32, 36, 39, 46, 47, 48, 49, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 23, 29, 32, 36, 39, 44, 46, 47, 48, 49, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 23, 26, 32, 36, 39, 46, 49, 50, 51, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 23, 26, 28, 32, 36, 39, 44, 46, 50, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 23, 25, 29, 32, 36, 39, 47, 49, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 23, 25, 29, 32, 36, 39, 44, 47, 49, 59, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 21, 23, 25, 26, 28, 36, 39, 50, 51, 52, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 18, 21, 24, 25, 27, 32, 34, 36, 40, 46, 51, 54, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 18, 21, 24, 25, 27, 28, 32, 34, 36, 40, 46, 49, 54, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 19, 21, 24, 25, 27, 32, 37, 39, 46, 51, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 19, 21, 24, 25, 27, 32, 34, 37, 39, 46, 51, 54, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 19, 21, 24, 25, 27, 28, 32, 37, 39, 46, 49, 53, 54, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 19, 21, 24, 25, 27, 28, 32, 34, 37, 39, 46, 49, 54, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 19, 20, 23, 28, 30, 34, 36, 37, 38, 39, 44, 45, 49, 51, 54, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 18, 19, 20, 23, 28, 30, 34, 36, 37, 38, 41, 45, 49, 51, 54, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 16, 18, 20, 23, 28, 30, 34, 36, 40, 44, 45, 49, 51, 54, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 15, 19, 20, 23, 28, 30, 34, 37, 39, 44, 45, 49, 51, 54, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 15, 18, 19, 20, 23, 28, 30, 34, 37, 41, 45, 49, 51, 54, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 13, 15, 16, 18, 20, 23, 28, 30, 34, 38, 40, 45, 49, 51, 54, 57, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 28, 29, 30, 34, 38, 40, 43, 45, 51, 52, 54, 56, 57, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 18, 20, 23, 27, 29, 30, 34, 38, 40, 44, 45, 50, 52, 54, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 19, 20, 23, 28, 30, 34, 35, 38, 40, 44, 50, 52, 55, 56, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 14, 19, 20, 23, 28, 31, 34, 38, 39, 44, 45, 50, 52, 53, 55, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 14, 18, 19, 20, 23, 28, 31, 34, 38, 41, 45, 50, 52, 53, 55, 56, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 18, 19, 20, 28, 31, 35, 38, 41, 44, 50, 52, 53, 56, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 18, 19, 20, 23, 28, 31, 35, 38, 41, 43, 45, 50, 52, 53, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 17, 19, 20, 23, 28, 31, 35, 38, 40, 44, 45, 50, 52, 53, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 17, 19, 20, 23, 28, 31, 34, 35, 38, 40, 45, 50, 52, 55, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 29, 32, 34, 38, 40, 43, 45, 49, 54, 56, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 18, 20, 23, 27, 29, 32, 34, 38, 40, 45, 50, 54, 56, 57, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 19, 20, 23, 28, 32, 35, 38, 40, 44, 50, 53, 56, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 17, 19, 20, 23, 29, 32, 34, 36, 37, 38, 40, 44, 45, 49, 52, 54, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 17, 19, 20, 23, 28, 29, 32, 34, 36, 37, 38, 40, 45, 51, 52, 54, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 16, 17, 19, 20, 23, 28, 32, 34, 35, 36, 40, 44, 50, 52, 55, 56, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 15, 17, 19, 20, 23, 29, 32, 34, 37, 40, 44, 45, 49, 52, 54, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 15, 17, 19, 20, 23, 28, 29, 32, 34, 37, 40, 45, 51, 52, 54, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 15, 16, 17, 19, 20, 23, 28, 32, 35, 38, 40, 44, 50, 52, 53, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 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38, 39, 40, 41, 43, 48, 49, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 19, 30, 32, 37, 40, 45, 48, 53, 55, 57, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 30, 32, 33, 35, 37, 39, 45, 48, 49, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 28, 30, 32, 37, 43, 44, 45, 48, 49, 53, 56, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 27, 29, 30, 32, 37, 39, 43, 44, 48, 49, 56, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 27, 28, 30, 32, 37, 44, 45, 48, 50, 53, 56, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 32, 35, 37, 39, 43, 44, 48, 53, 54, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 32, 33, 35, 37, 39, 43, 48, 49, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 21, 25, 35, 39, 42, 44, 46, 48, 53, 55, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 19, 30, 32, 34, 37, 44, 48, 49, 53, 56, 57, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 21, 25, 35, 41, 42, 44, 46, 48, 53, 55, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 32, 34, 35, 36, 39, 41, 52, 54, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 25, 35, 38, 45, 48, 53, 54, 55, 57, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 25, 34, 35, 36, 44, 45, 46, 53, 54, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 25, 34, 35, 36, 39, 46, 54, 55, 58, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 25, 33, 34, 38, 43, 44, 48, 53, 54, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 25, 33, 34, 35, 38, 45, 48, 49, 53, 57, 58, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 25, 28, 30, 34, 35, 36, 39, 41, 52, 54, 57, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 25, 27, 28, 38, 43, 44, 48, 50, 51, 53, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 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36, 40, 44, 45, 52, 53, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 32, 34, 36, 39, 40, 52, 55, 58, 59, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 25, 34, 36, 39, 40, 41, 46, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 25, 32, 38, 40, 45, 52, 53, 55, 57, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 25, 28, 30, 34, 36, 39, 40, 52, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 23, 25, 32, 34, 38, 39, 40, 52, 53, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 32, 35, 36, 39, 44, 45, 52, 54, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 30, 33, 38, 41, 43, 44, 52, 53, 54, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 25, 32, 33, 38, 39, 43, 44, 52, 54, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 25, 32, 33, 35, 38, 39, 45, 49, 52, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 19, 25, 36, 39, 40, 44, 45, 46, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 30, 34, 38, 40, 43, 44, 52, 53, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 25, 38, 40, 41, 43, 44, 48, 53, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 25, 32, 38, 40, 43, 44, 52, 53, 55, 62, 63 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1305
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS158[5], DS158[6], DS158[7], DS158[8], DS158[11], DS158[13], DS158[15], DS158[16], DS158[18], DS158[20], DS158[22], DS158[23], DS158[25], DS158[26], DS158[27], DS158[33], DS158[34], DS158[40], DS158[41], DS158[43], DS158[44], DS158[45], DS158[46], DS158[47], DS158[50], DS158[51], DS158[52], DS158[53], DS158[54], DS158[55], DS158[56], DS158[58], DS158[59], DS158[61], DS158[62], DS158[64], DS158[65], DS158[66], DS158[69], DS158[70], DS158[71], DS158[72], DS158[74], DS158[81], DS158[82], DS158[83], DS158[84], DS158[85], DS158[86], DS158[87], DS158[93], DS158[94], DS158[95], DS158[97], DS158[99], DS158[100], DS158[102], DS158[103], DS158[104], DS158[106], DS158[107], DS158[108], DS158[109], DS158[111], DS158[112], DS158[113], DS158[115], DS158[116], DS158[121], DS158[122], DS158[123], DS158[124], DS158[125], DS158[128], DS158[132], DS158[138], DS158[139], DS158[140], DS158[141], DS158[143], DS158[144], DS158[145], DS158[149], DS158[151], DS158[157], DS158[162], DS158[165], DS158[167], DS158[169], DS158[171], DS158[172], DS158[174], DS158[175], DS158[177], DS158[178], DS158[179], DS158[181], DS158[184], DS158[187], DS158[188], DS158[195], DS158[198], DS158[199], DS158[200], DS158[201], DS158[208], DS158[209], DS158[210], DS158[213], DS158[214], DS158[224], DS158[228], DS158[229], DS158[239], DS158[240], DS158[242], DS158[243], DS158[244], DS158[247], DS158[248], DS158[249], DS158[250], DS158[251], DS158[252], DS158[253], DS158[255], DS158[260], DS158[261], DS158[262], DS158[263], DS158[270], DS158[271], DS158[274], DS158[275], DS158[280], DS158[283], DS158[285], DS158[286], DS158[292], DS158[293], DS158[296], DS158[298], DS158[306], DS158[309], DS158[315], DS158[319], DS158[321], DS158[322], DS158[323], DS158[324], DS158[325], DS158[326], DS158[327], DS158[328], DS158[329], DS158[330], DS158[331], DS158[332], DS158[335], DS158[337], DS158[338], DS158[339], DS158[342], DS158[346], DS158[347], DS158[348], DS158[349], DS158[350], DS158[352], DS158[358], DS158[359], DS158[360], DS158[362], DS158[365], DS158[367], DS158[369], DS158[370], DS158[371], DS158[372], DS158[373], DS158[374], DS158[375], DS158[376], DS158[377], DS158[378], DS158[379], DS158[380], DS158[383], DS158[385], DS158[387], DS158[388], DS158[389], DS158[390], DS158[392], DS158[396], DS158[397], DS158[398], DS158[399], DS158[400], DS158[401], DS158[404], DS158[405], DS158[406], DS158[407], DS158[408], DS158[409], DS158[411], DS158[412], DS158[413], DS158[414], DS158[415], DS158[416], DS158[417], DS158[418], DS158[419], DS158[420], DS158[421], DS158[422], DS158[423], DS158[424], DS158[426], DS158[427], DS158[428], DS158[429], DS158[434], DS158[436], DS158[438], DS158[439], DS158[440], DS158[441], DS158[442], DS158[444], DS158[447], DS158[449], DS158[451], DS158[453], DS158[455], DS158[456], DS158[460], DS158[464], DS158[466], DS158[470], DS158[476], DS158[479], DS158[480], DS158[481], DS158[482], DS158[484], DS158[489], DS158[490], DS158[491], DS158[492], DS158[493], DS158[497], 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# Note that there is no reversible (64,28,12) difference sets in  
# group [64,158].
  
  
  
   
   
###########################  
###########################  
###########################