On a conjecture in D-optimal designs with n ≡ 0 mod 4

This paper is devoted to analyze a conjecture in D-optimal designs proposed by Bora-Senta and Moyssiadis [An algorithm for finding exact D- and A-optimal designs with n observations and k two-level factors in the presence of autocorrelated errors, J. Combin. Math. Combin. Comput. 30 (1999) 149-170] in 1999. With the aid of techniques of differential calculus, Hadamard's and Fisher's inequalities for symmetric and positive definite matrices, we prove that the conjecture is true for n autocorrelated observations and k two-level factors with n = 4ν and k = 2.