Notes on D-optimal designs

The purpose of this paper is to exhibit new infinite families of D-optimal (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 m. 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 show that for a given j and d sufficiently large, about half of the entries in each column of a D-optimal matrix are ones. This leads to a new 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.