KOUKOUVINOS CHRISTOS Oct 23, 99 04:17:14 pm +0300

D-optimal Designs

This list contains the (0,1) incidence matrices of SBIBD(2s^2+2s+1, s^2, s(s-1)/2), where s=1,2,3,4,5. We note that the (1,-1) incidence matrices of these SBIBD's are exactly the D-optimal designs of order 5,13,25,41,61 respectively.

s=1 : (5,1,0) This designs is trivial. The (0,1) incidence matrix is circulant with first row:

1 0 0 0 0

(i.e. the identity matrix I of order 5)

s=2 : (13,4,1) The (0,1) incidence matrix is circulant with first row:

1 1 0 1 0 0 0 0 0 1 0 0 0

s=3 : (25,9,3) The (0,1) incidence matrix is:

1111111110000000000000000
1110000000000110011001100
1110000000000001100110011
1001001001100110000110000
1001001000011001111000000
1000100011100000011000011
1000100010011000000111100
1000010101100001100001100
1000010100011110000000011
0101000011010010100001010
0101000010101101000000101
0100100101010101001010000
0100100100101010110100000
0100011001010000010100101
0100011000101000001011010
0011000101001000010010110
0011000100110000001101001
0010101001001011000001001
0010101000110100100000110
0010010011001100101100000
0010010010110011010010000
0001110000000101010101010
0001110000000010101010101
0000001110000100110011001
0000001110000011001100110

s=4 : (41,16,6) The (0,1) incidence matrix is:

1111111111111110 0000000000000000 000000001
0001011000001011 0000100000111111 000101001
0000101100100100 1000010001011101 100010101
1000000110010010 0100001001101100 110001011
0100000011101000 0010000101110100 011100101
0010010001010100 0001000011111010 001010011
0010100010110000 1111100001000011 000101001
1001000001011001 0111010000100001 100010101
0100110000001101 1011001000010000 110001011
1010001000000111 1101000100001000 011100101
0101000100100011 1110000010000110 001010011
1100000101000101 0000011111000011 000101001
0110010010000010 1000101110100001 100010101
0011001001100000 0100110110010000 110001011
0001110100010000 0010111010001000 011100101
1000101010001000 0001111100000110 001010011
0000011010001110 0110010011000011 010000110
0000001101100110 0011101000100001 101100010
0000010110110011 0001010100010010 110110000
0000001011111001 1000001010001001 011011000
0000010101011100 1100100100000110 101001100
0011100000110101 0000001100100111 010000110
1001100000011010 1000000111010001 101100010
1100100000101100 0100100010101010 110110000
1110000000010110 0010110000010101 011011000
0111000000101010 0001011001001010 101001100
1101000111000000 1001100000011011 010000110
0110110011000001 0100010000001101 101100010
1011011001000000 1010001001000110 110110000
0101111100000000 0101000101100001 011011000
1010101110000001 0010000010110010 101001100
1010010100101000 0111001110011101 000000000
0101001010010101 0011100111001100 100000000
0010100101001011 1001110011100100 010000000
1001010010100101 1100111001110000 001000000
0100101001010010 1110011100111010 000000000
1100011000110000 1001010010100100 000101110
0110001100011001 0100101001010000 000110110
0011000110001100 1010010100101000 000111010
0001100011000110 0101001010010100 000111100
1000110001100011 0010100101001000 000011110

s=5: (61,25,10) The (0,1) incidence matrix can be found in SBIBD Library.

Created 24th October 1999 by matrices supplied by Dr Christos Koukouvinos.