Abstract

Doptimal designs of order n = 2 v ≡ 2 (mod 4), where q is a prime power and v = q2 + q + 1 are constructed using two methods, one with supplementary difference sets and the other using projective planes more directly. An infinite family of Hadamard matrices of order n = 4v with maximum excess σ(n) = n n3 where q is a prime power and v = q2 + q + 1 is a prime, is also constructed. © 1991.