D-optimal and near D-optimal fractional factorial designs of resolution V

Upper bounds for the determinant of the information matrix of a 2 k fractional factorial design of resolution V are improved. Highly D-efficient 2 k fractional factorial designs of resolution V for 3 ⩽ k ⩽ 8 are found using the heuristic algorithms of Nguyen and Miller [1992. A review of some exchange algorithms for constructing discrete D -optimal designs. Comput. Statist. Data Anal. 14, 489–498] and Miller and Nguyen [1994. Algorithm AS 295: a Fedorov exchange algorithm for D -optimal designs. Appl. Statist. 43, 669–678]. Some of these designs are shown to be D-optimal or generalized type 1 (type 2) optimal. A method for constructing D-optimal or nearly D-optimal resolution V designs from smaller D-optimal or nearly D-optimal resolution V designs is presented. Lower bounds for D-efficiencies are tabulated.