D-optimal and near D -optimal 2k2k fractional factorial designs of resolution V

Upper bounds for the determinant of the information matrix of a 2k2k fractional factorial design of resolution V are improved. Highly D  -efficient 2k2k fractional factorial designs of resolution V for 3⩽k⩽83⩽k⩽8 are found using the heuristic algorithms of Nguyen and Miller [1992. A review of some exchange algorithms for constructing discrete DD-optimal designs. Comput. Statist. Data Anal. 14, 489–498] and Miller and Nguyen [1994. Algorithm AS 295: a Fedorov exchange algorithm for DD-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.