Best double circulant found so far for 54

110001001011000100111110101011101010010011111011110010
111000100101100010011111010001110101001001111101111001
011100010010110001001111101100111010100100111110111100
101110001001011000100111110010011101010010011111011110
010111000100101100010011111001001110101001001111101111
101011100010010110001001111100100111010100100111110111
110101110001001011000100111110010011101010010011111011
111010111000100101100010011111001001110101001001111101
111101011100010010110001001111100100111010100100111110
111110101110001001011000100011110010011101010010011111
011111010111000100101100010101111001001110101001001111
001111101011100010010110001110111100100111010100100111
100111110101110001001011000111011110010011101010010011
010011111010111000100101100111101111001001110101001001
001001111101011100010010110111110111100100111010100100
000100111110101110001001011011111011110010011101010010
100010011111010111000100101001111101111001001110101001
110001001111101011100010010100111110111100100111010100
011000100111110101110001001010011111011110010011101010
101100010011111010111000100001001111101111001001110101
010110001001111101011100010100100111110111100100111010
001011000100111110101110001010010011111011110010011101
100101100010011111010111000101001001111101111001001110
010010110001001111101011100010100100111110111100100111
001001011000100111110101110101010010011111011110010011
000100101100010011111010111110101001001111101111001001
100010010110001001111101011111010100100111110111100100
001001111011111001001010111001010000011011100101101110
100100111101111100100101011000101000001101110010110111
110010011110111110010010101100010100000110111001011011
111001001111011111001001010110001010000011011100101101
011100100111101111100100101111000101000001101110010110
101110010011110111110010010011100010100000110111001011
010111001001111011111001001101110001010000011011100101
101011100100111101111100100110111000101000001101110010
010101110010011110111110010011011100010100000110111001
001010111001001111011111001101101110001010000011011100
100101011100100111101111100010110111000101000001101110
010010101110010011110111110001011011100010100000110111
001001010111001001111011111100101101110001010000011011
100100101011100100111101111110010110111000101000001101
110010010101110010011110111111001011011100010100000110
111001001010111001001111011011100101101110001010000011
111100100101011100100111101101110010110111000101000001
111110010010101110010011110110111001011011100010100000
011111001001010111001001111011011100101101110001010000
101111100100101011100100111001101110010110111000101000
110111110010010101110010011000110111001011011100010100
111011111001001010111001001000011011100101101110001010
111101111100100101011100100000001101110010110111000101
011110111110010010101110010100000110111001011011100010
001111011111001001010111001010000011011100101101110001
100111101111100100101011100101000001101110010110111000
010011110111110010010101110010100000110111001011011100

M M^T:

 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 17 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 17 16 16 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 16 16 16 17 16 16 30 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15 16
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15 16
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15 16
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29 15
 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 15 15 16 15 15 15 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 15 15 16 15 15 29

Determinant 22572298204370013622299470489600 (2.25723e+31) set 1593 result 8.89496e+24
A = 13 B = 16 N = 27

 13  6  6  6  6  6  6  6  6  6  7  7  4  6
 16  9  9 10  9  9  9  9  9 10  8  8 12  9
 29 15 15 16 15 15 15 15 15 16 15 15 16 15