Supplementary difference sets and optimal designs

D-optimal designs of order n = 2v ≡ 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 (n) = n√n 3 where q is a prime power and v = q2 + q + 1 is a prime, is also constructed. Disciplines Physical Sciences and Mathematics Publication Details Christos Koukouvinos, Stratis Kounias, and Jennifer Seberry, Supplementary difference sets and optimal designs, Discrete Mathematics, 87, (1991), 49-58. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1052 Discrete Mathematics 88 (1991) 49-58 North-Holland 49 Supplementary difference sets and optimal designs Christos Koukouvinos Department of Mathematics, University of Thessaloniki, Thessaloniki, 54006, Greece Stratis Kounias Department of Statistics, University of Athens, Athens, 15784, Greece Jennifer Seberry Department of Computer Science, University College, University of New South Wales, Australian Defence Force Academy, A.C. T. 2600, Australia Received 31 October 1988 Abstract Koukouvinos, c., S. Kounias and 1. Seberry, Supplementary difference sets and optimal designs, Discrete Mathematics 49-58. D-optimal designs of order n = 2v == 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 a(n) = nYn 3 where q is a prime power and v = q2 + q + 1 is a prime, is also constructed.Koukouvinos, c., S. Kounias and 1. Seberry, Supplementary difference sets and optimal designs, Discrete Mathematics 49-58. D-optimal designs of order n = 2v == 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 a(n) = nYn 3 where q is a prime power and v = q2 + q + 1 is a prime, is also constructed.