Disciplines

Existence of SBIBD(4k2, 2k2 + k, k2 + k) and Hadamard matrices with maximal excess It is shown that SBIBD ( 4k2, 2k2 ± k, k2 ± k) and Hadamard matrices with maximal excess exist for k = qs, q ∑{q: q ≡ 1 (mod 4) is a prime power}, s ∑ {I,...,33, 37,...,41,45,...,59} U {2g + 1,g the length of a Golay sequence}. This leaves the following odd k < 250 undecided 47,71,77,79,103,107;127,131,133,139, 141,151,163,167,177,179,191,199,209,...,217,223,227, 231,233,237,239,243,249. There is also a proper n dimensional Hadamard matrix of order (4k2)n. Regular symmetric Hadamard matrices with constant diagonal are obtained for orders 4k2 whenever complete regular 4-sets of regular matrices of order k2 exist