NOTES ON D-OPTIMAL DESIGNS

The purpose of this paper is to exhibit new infinite families of D-opt imal (0, 1)-matrices. We show that Hadamard designs lead to D-optimal matrices of size (j, mj) and (j - 1, mj), for certain integers j = 3 ( mod 4) and all positive integers in. For j a power of a prime and j = 1 (mod 4), supplementary difference sets lead to D-optimal matrices of size (j, 2mj) and (j - 1,2mj), for all positive integers m. We also s how that for a given j and d sufficiently large, about half of the ent ries in each column of a D-optimal matrix are ones. This leads to a ne w relationship between D-optimality for (0, 1)-matrices and for (+/-1) -matrices. Known results about D-optimal (+/-1)-matrices are then used to obtain new D-optimal (0, 1)-matrices. (C) 1998 Elsevier Science In c. All rights reserved.