D-Optimal Saturated Factorial Designs with Three Factors

The aim of this paper is to study the D-optimal m1×m2×m3, m3≥m2≥m1≥2 saturated factorial designs for estimating the mean and the main effects. A restricted class D of m1×m2×m3 saturated designs is defined. In this class, the upper bounds of the determinant values of D-optimal matrices for the already known 2×m2×m3, m3≥m2≥2, 3×m2×m2, m2≥3, 3×m2×(m2+1), m2≥3 and for 4×4×m3, m3≥4 saturated designs are found. New results regarding the determinant values of D-optimal matrices and the designs achieving them are presented for the 4×5×m3, m3≥5 and 4×6×m3, m3≥6 saturated factorial designs in D.