### 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 [64,148]. 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 [64,148].
    
    
# 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(64,148));' can be 
# used to create a list e of the elements of the group [64,148].
# In our list of (64,28,12) DSs in group [64,148], we have [1, 
# 2, 3, 4, 5, 9, 10, 11, 13, 14, 18, 22, 23, 29, 34, 
# 35, 36, 38, 40, 42, 43, 45, 49, 52, 55, 57, 59, 62].
# This list denotes the elements [ e[1], e[2], e[3], 
# e[4], e[5], e[9], e[10], e[11], e[13], e[14], e[18], e[22], e[23], e[29], e[34], e[35], 
# e[36], e[38], e[40], e[42], e[43], e[45], e[49], e[52], e[55], e[57], e[59], e[62]]
# where e is the list of the elements of the group [64,148] as they 
# appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,148));'
    
    
###########################  
###########################  
###########################  
  
### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs
### that rise from these DSs in group [64, 148]
  
  
  
### The number of inequivalent (64,28,12) DSs in group [64,148] is 1900
### The list of all inequivalent (64,28,12) DSs in group [64,148] is 
  
  
DS148:=[ [ 1, 2, 3, 4, 5, 9, 10, 11, 13, 14, 18, 22, 23, 29, 34, 35, 36, 38, 40, 42, 43, 45, 49, 52, 55, 57, 59, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 16, 18, 22, 23, 28, 29, 30, 37, 40, 42, 43, 44, 46, 47, 48, 51, 52, 57, 58 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 14, 16, 17, 18, 22, 23, 24, 28, 29, 30, 37, 39, 42, 43, 44, 48, 51, 52, 58, 61 ], [ 1, 2, 3, 4, 5, 8, 9, 12, 13, 14, 18, 22, 24, 25, 27, 29, 30, 34, 35, 36, 38, 40, 42, 50, 52, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 14, 16, 18, 22, 26, 27, 28, 32, 37, 40, 42, 43, 46, 49, 52, 57, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 14, 16, 17, 18, 22, 26, 27, 28, 32, 37, 39, 42, 43, 46, 49, 52, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 14, 15, 17, 19, 22, 26, 27, 28, 32, 36, 40, 42, 43, 46, 49, 52, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 22, 24, 26, 28, 32, 34, 35, 36, 40, 42, 47, 50, 52, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 22, 24, 26, 27, 28, 32, 34, 35, 36, 40, 42, 47, 49, 52, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 22, 24, 25, 27, 29, 32, 34, 35, 36, 40, 42, 46, 50, 52, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 25, 27, 29, 32, 33, 34, 36, 41, 42, 47, 50, 52, 53, 56, 61 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 24, 26, 28, 32, 33, 34, 36, 41, 42, 47, 50, 52, 53, 56, 62 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 24, 26, 27, 28, 32, 33, 34, 36, 41, 42, 47, 49, 52, 53, 56 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 22, 24, 25, 27, 29, 32, 33, 34, 36, 41, 42, 46, 50, 52, 53, 56 ], [ 1, 2, 3, 4, 5, 8, 9, 10, 13, 16, 18, 19, 20, 22, 24, 27, 29, 32, 33, 34, 36, 41, 46, 48, 50, 52, 53, 56 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 18, 19, 21, 23, 29, 32, 33, 34, 36, 37, 38, 41, 43, 44, 49, 52, 53, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 16, 18, 21, 23, 32, 34, 35, 36, 40, 43, 44, 49, 50, 51, 52, 55, 56, 57, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 16, 18, 19, 21, 23, 32, 33, 34, 36, 41, 43, 44, 49, 50, 51, 52, 53, 56, 58 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 18, 21, 23, 29, 32, 34, 35, 38, 40, 44, 49, 52, 55, 56, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 18, 21, 23, 29, 32, 34, 35, 38, 40, 43, 44, 49, 52, 55, 56, 57, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 13, 14, 18, 19, 21, 23, 29, 32, 33, 34, 38, 41, 43, 44, 49, 52, 53, 56, 58, 62 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 14, 19, 21, 23, 28, 30, 33, 34, 35, 38, 39, 44, 45, 50, 56, 57, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 19, 21, 23, 30, 33, 38, 39, 43, 44, 49, 50, 51, 53, 55, 57, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 21, 23, 29, 30, 33, 38, 41, 43, 44, 49, 53, 55, 57, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 19, 21, 23, 28, 30, 38, 39, 44, 45, 50, 53, 54, 55, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 18, 21, 28, 30, 34, 35, 36, 37, 38, 40, 46, 47, 48, 50, 52, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 18, 19, 21, 24, 27, 28, 30, 33, 34, 36, 37, 38, 41, 48, 49, 52, 53, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 15, 16, 17, 21, 24, 25, 27, 30, 33, 38, 41, 46, 49, 51, 52, 53, 55, 57 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 14, 18, 21, 28, 30, 34, 35, 38, 40, 46, 47, 48, 50, 52, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 14, 18, 21, 24, 28, 30, 34, 35, 38, 40, 48, 50, 52, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 14, 18, 21, 24, 27, 28, 30, 34, 35, 38, 40, 48, 49, 52, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 14, 18, 19, 21, 24, 27, 28, 30, 33, 34, 38, 41, 48, 49, 52, 53, 56, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 19, 21, 25, 26, 27, 28, 31, 33, 34, 35, 38, 39, 48, 49, 52, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 19, 25, 26, 27, 28, 31, 37, 38, 39, 40, 42, 48, 49, 52, 53, 55, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 19, 21, 25, 26, 27, 28, 31, 38, 39, 48, 49, 52, 53, 54, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 17, 18, 21, 23, 24, 25, 27, 32, 36, 46, 49, 51, 56, 57, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 21, 23, 26, 27, 32, 36, 39, 41, 46, 49, 51, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 21, 23, 24, 25, 32, 36, 41, 45, 46, 49, 50, 51, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 21, 23, 24, 25, 29, 32, 36, 41, 46, 49, 57, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 21, 23, 24, 25, 29, 32, 36, 41, 43, 46, 49, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 21, 23, 24, 25, 27, 32, 36, 41, 45, 46, 51, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 18, 19, 21, 26, 28, 32, 35, 36, 37, 38, 41, 46, 50, 52, 54, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 18, 21, 26, 28, 29, 32, 38, 40, 45, 46, 51, 52, 56, 57, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 18, 21, 23, 26, 28, 29, 32, 38, 40, 43, 44, 46, 51, 52, 56, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 18, 19, 21, 26, 27, 28, 32, 35, 38, 41, 46, 49, 52, 54, 55, 56, 61, 63 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 17, 18, 21, 26, 28, 29, 32, 38, 39, 45, 46, 51, 52, 56, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 17, 18, 21, 26, 27, 28, 32, 38, 39, 43, 46, 49, 52, 56, 58, 59, 61, 64 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 17, 18, 21, 23, 26, 28, 32, 38, 39, 44, 45, 46, 50, 52, 56, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 17, 18, 21, 23, 26, 28, 29, 32, 38, 39, 43, 44, 46, 51, 52, 56, 58, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 15, 19, 21, 23, 24, 28, 32, 39, 44, 45, 46, 48, 50, 52, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 14, 15, 17, 18, 21, 23, 24, 29, 32, 39, 44, 45, 46, 48, 49, 52, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 18, 19, 21, 26, 28, 32, 33, 34, 36, 37, 38, 41, 46, 50, 52, 53, 61, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 18, 19, 21, 26, 27, 28, 32, 33, 34, 36, 37, 38, 41, 46, 49, 52, 53, 61 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 18, 19, 21, 24, 25, 29, 32, 33, 34, 36, 37, 38, 41, 46, 49, 52, 53, 62 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 16, 18, 21, 24, 25, 32, 34, 35, 36, 40, 46, 49, 50, 51, 52, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 7, 8, 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25, 27, 50, 51, 52, 54, 55, 56, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 20, 21, 27, 32, 34, 38, 45, 46, 49, 55, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 31, 32, 38, 41, 50, 52, 53, 54, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 27, 32, 37, 38, 41, 49, 50, 53, 56, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 22, 29, 30, 33, 35, 36, 41, 42, 48, 49, 54, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 22, 27, 29, 30, 35, 36, 41, 42, 48, 50, 53, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 21, 22, 25, 27, 30, 37, 41, 50, 51, 53, 54, 55, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 21, 22, 25, 27, 29, 30, 37, 41, 53, 54, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 20, 22, 26, 27, 29, 31, 36, 41, 53, 54, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 20, 22, 26, 31, 36, 49, 50, 51, 53, 55, 58, 59, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 20, 22, 26, 31, 36, 43, 49, 50, 51, 53, 55, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 18, 22, 29, 33, 35, 42, 48, 49, 52, 54, 56, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 18, 22, 27, 29, 35, 42, 48, 50, 52, 53, 56, 59, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 28, 32, 36, 38, 40, 50, 51, 54, 56, 57, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 23, 29, 32, 36, 38, 40, 49, 51, 54, 56, 57, 58, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 20, 28, 29, 31, 42, 45, 47, 51, 53, 55, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 23, 32, 36, 38, 41, 49, 50, 54, 56, 58, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 30, 37, 39, 40, 43, 46, 47, 49, 52, 53, 55, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 19, 30, 37, 38, 40, 41, 46, 49, 52, 53, 54, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 18, 19, 30, 33, 34, 37, 38, 43, 49, 52, 53, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 30, 36, 38, 39, 41, 46, 49, 52, 53, 54, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 30, 33, 38, 39, 41, 43, 49, 52, 53, 55, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 30, 33, 35, 38, 46, 49, 52, 53, 54, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 30, 33, 35, 36, 38, 43, 49, 52, 54, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 20, 28, 33, 34, 36, 42, 45, 47, 51, 54, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 20, 27, 29, 33, 34, 36, 42, 44, 47, 51, 54, 57, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 27, 30, 33, 34, 37, 41, 52, 54, 57, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 18, 30, 33, 35, 37, 41, 44, 46, 52, 54, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 30, 34, 35, 37, 40, 44, 46, 52, 55, 57, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 27, 30, 33, 34, 35, 37, 39, 52, 55, 57, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 20, 29, 33, 42, 44, 47, 51, 53, 55, 56, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 20, 27, 34, 35, 36, 42, 45, 47, 49, 55, 58, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 20, 27, 28, 33, 42, 45, 47, 51, 53, 55, 56, 58, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 19, 30, 33, 34, 37, 41, 44, 46, 52, 53, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 27, 30, 33, 35, 37, 41, 52, 53, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 19, 26, 30, 33, 39, 41, 43, 48, 50, 52, 55, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 18, 19, 26, 30, 35, 46, 48, 50, 52, 53, 57, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 18, 19, 25, 30, 34, 47, 48, 50, 52, 54, 57, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 18, 19, 25, 27, 37, 38, 39, 43, 45, 46, 49, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 30, 36, 37, 39, 40, 46, 49, 52, 53, 54, 55, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 30, 33, 37, 39, 40, 43, 49, 52, 53, 55, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 25, 28, 29, 37, 38, 39, 45, 46, 49, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 25, 26, 27, 30, 39, 44, 45, 46, 52, 54, 55, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 24, 30, 39, 40, 43, 46, 49, 52, 55, 59, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 19, 25, 26, 30, 41, 43, 52, 53, 55, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 18, 25, 26, 27, 30, 41, 43, 52, 54, 55, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 18, 19, 30, 34, 35, 37, 46, 49, 52, 53, 55, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 18, 19, 30, 34, 35, 36, 37, 43, 49, 52, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 30, 33, 38, 40, 41, 43, 49, 52, 53, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 30, 33, 38, 39, 41, 50, 52, 54, 55, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 19, 30, 35, 38, 46, 50, 52, 53, 54, 57, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 30, 34, 38, 46, 49, 52, 53, 54, 59, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 19, 27, 35, 37, 39, 46, 48, 49, 53, 54, 55, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 28, 29, 33, 35, 37, 39, 46, 48, 49, 55, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 30, 33, 41, 52, 53, 55, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 27, 30, 33, 41, 52, 54, 55, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 29, 34, 36, 37, 40, 42, 47, 49, 51, 53, 55, 56, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 25, 29, 33, 40, 42, 43, 48, 49, 51, 56, 59, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 26, 30, 37, 40, 41, 46, 48, 50, 52, 53, 58, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 30, 34, 37, 38, 39, 40, 46, 50, 52, 54, 55, 57, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 34, 36, 38, 40, 42, 47, 49, 50, 53, 55, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 27, 34, 36, 38, 39, 42, 47, 49, 50, 54, 55, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 24, 34, 38, 40, 42, 43, 49, 50, 55, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 24, 27, 33, 34, 38, 39, 42, 49, 50, 55, 56, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 30, 37, 38, 40, 41, 46, 50, 52, 53, 54, 58, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 30, 33, 37, 38, 39, 41, 46, 49, 52, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 30, 34, 37, 38, 39, 40, 46, 49, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 20, 27, 35, 37, 38, 39, 42, 47, 49, 50, 53, 55, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 30, 33, 38, 40, 41, 43, 49, 52, 54, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 30, 33, 36, 38, 40, 41, 46, 49, 52, 53, 54, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 35, 36, 38, 39, 40, 46, 49, 52, 54, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 30, 33, 35, 38, 39, 40, 43, 49, 52, 55, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 28, 29, 34, 36, 40, 42, 45, 47, 55, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 37, 40, 41, 43, 49, 52, 55, 56, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 36, 37, 40, 41, 46, 49, 52, 53, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 30, 34, 36, 37, 39, 41, 46, 50, 52, 54, 55, 58, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 25, 26, 27, 30, 41, 43, 52, 53, 57, 58, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 24, 25, 30, 39, 41, 43, 48, 50, 52, 58, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 35, 36, 37, 39, 41, 46, 49, 52, 54, 55, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 30, 33, 35, 37, 39, 41, 43, 49, 52, 55, 56, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 26, 30, 40, 41, 43, 48, 50, 52, 58, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 25, 26, 30, 41, 43, 52, 54, 57, 59, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 30, 34, 35, 36, 37, 50, 52, 57, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 30, 33, 34, 38, 39, 40, 50, 52, 55, 57, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 30, 33, 38, 40, 41, 50, 52, 53, 60, 61, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 30, 33, 38, 39, 41, 43, 49, 52, 54, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 30, 34, 38, 39, 40, 43, 49, 52, 55, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 24, 27, 35, 38, 39, 42, 49, 50, 55, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 27, 30, 33, 41, 52, 53, 57, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 30, 33, 41, 52, 54, 57, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 34, 40, 52, 55, 57, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 27, 30, 35, 39, 52, 55, 57, 58, 60, 61, 63 ] ];
  
  
### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 1062
### These  nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: 
### DS148[1], DS148[3], DS148[7], DS148[10], DS148[11], DS148[13], DS148[15], DS148[17], DS148[18], DS148[19], DS148[20], DS148[22], DS148[23], DS148[27], DS148[28], DS148[36], DS148[37], DS148[41], DS148[48], DS148[50], DS148[51], DS148[54], DS148[56], DS148[57], DS148[59], DS148[60], DS148[61], DS148[65], DS148[66], DS148[67], DS148[69], DS148[70], DS148[72], DS148[75], DS148[77], DS148[80], DS148[82], DS148[84], DS148[88], DS148[89], DS148[90], DS148[91], DS148[92], DS148[96], DS148[99], DS148[100], DS148[106], DS148[107], DS148[109], DS148[113], DS148[114], DS148[127], DS148[130], DS148[135], DS148[139], DS148[141], DS148[142], DS148[143], DS148[153], DS148[154], DS148[156], DS148[159], DS148[161], DS148[162], DS148[164], DS148[165], DS148[169], DS148[177], DS148[182], DS148[183], DS148[184], DS148[187], DS148[191], DS148[198], DS148[200], DS148[202], DS148[204], DS148[207], DS148[212], DS148[213], DS148[214], DS148[215], DS148[216], DS148[229], DS148[247], DS148[248], DS148[254], DS148[256], DS148[257], DS148[258], DS148[259], DS148[263], DS148[266], DS148[268], DS148[271], DS148[272], DS148[273], DS148[274], DS148[276], DS148[280], DS148[281], DS148[283], DS148[286], DS148[287], DS148[292], DS148[302], DS148[307], DS148[313], DS148[314], DS148[329], DS148[331], DS148[332], DS148[333], DS148[335], DS148[341], DS148[342], DS148[343], DS148[346], DS148[349], DS148[350], DS148[353], DS148[355], DS148[356], DS148[362], DS148[363], DS148[364], DS148[365], DS148[366], DS148[378], DS148[382], DS148[383], DS148[384], DS148[387], DS148[390], DS148[392], DS148[394], DS148[395], DS148[401], DS148[402], DS148[404], DS148[409], DS148[411], DS148[417], DS148[418], DS148[421], DS148[422], DS148[423], DS148[425], DS148[429], DS148[430], DS148[437], DS148[438], DS148[439], DS148[442], DS148[443], DS148[448], DS148[452], DS148[454], DS148[456], DS148[457], DS148[458], DS148[459], DS148[461], DS148[462], DS148[464], DS148[465], DS148[466], DS148[467], DS148[470], DS148[471], DS148[472], DS148[473], DS148[474], DS148[475], DS148[476], DS148[478], DS148[481], DS148[482], DS148[484], DS148[485], DS148[490], DS148[491], DS148[492], DS148[493], DS148[500], DS148[504], DS148[505], DS148[506], DS148[512], DS148[520], DS148[522], DS148[526], DS148[530], DS148[538], DS148[539], DS148[542], DS148[543], DS148[557], DS148[559], DS148[562], DS148[567], DS148[568], DS148[569], DS148[570], DS148[571], DS148[572], DS148[577], DS148[581], DS148[582], DS148[589], DS148[590], DS148[594], DS148[595], DS148[603], DS148[604], DS148[605], DS148[608], DS148[609], DS148[610], DS148[614], DS148[617], DS148[619], DS148[620], DS148[624], DS148[627], DS148[629], DS148[630], DS148[631], DS148[632], DS148[636], DS148[637], DS148[638], DS148[641], DS148[642], DS148[643], DS148[644], DS148[646], DS148[647], DS148[648], DS148[649], DS148[655], DS148[660], DS148[664], DS148[666], DS148[667], DS148[669], DS148[674], DS148[675], DS148[678], DS148[679], DS148[682], DS148[684], DS148[685], 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DS148[1790], DS148[1791], DS148[1792], DS148[1793], DS148[1794], DS148[1795], DS148[1796], DS148[1799], DS148[1800], DS148[1801], DS148[1802], DS148[1804], DS148[1805], DS148[1806], DS148[1807], DS148[1808], DS148[1809], DS148[1810], DS148[1811], DS148[1812], DS148[1815], DS148[1816], DS148[1817], DS148[1818], DS148[1819], DS148[1821], DS148[1822], DS148[1823], DS148[1825], DS148[1826], DS148[1827], DS148[1828], DS148[1829], DS148[1830], DS148[1831], DS148[1832], DS148[1833], DS148[1834], DS148[1835], DS148[1836], DS148[1837], DS148[1838], DS148[1839], DS148[1840], DS148[1841], DS148[1842], DS148[1843], DS148[1844], DS148[1845], DS148[1846], DS148[1847], DS148[1848], DS148[1849], DS148[1850], DS148[1851], DS148[1852], DS148[1853], DS148[1854], DS148[1855], DS148[1856], DS148[1857], DS148[1858], DS148[1859], DS148[1860], DS148[1861], DS148[1862], DS148[1863], DS148[1864], DS148[1865], DS148[1866], DS148[1867], DS148[1868], DS148[1869], DS148[1870], DS148[1871], DS148[1872], DS148[1873], DS148[1874], DS148[1875], DS148[1876], DS148[1877], DS148[1878], DS148[1879], DS148[1880], DS148[1881], DS148[1882], DS148[1883], DS148[1884], DS148[1885], DS148[1886], DS148[1887], DS148[1888], DS148[1889], DS148[1890], DS148[1891], DS148[1892], DS148[1893], DS148[1894], DS148[1895], DS148[1896], DS148[1897], DS148[1898], DS148[1899], DS148[1900]. 
         
         
  
# Note that there is no reversible (64,28,12) difference sets in  
# group [64,148].
  
  
  
   
   
###########################  
###########################  
###########################