Resolution IV fractional factorial designs for the general asymmetric factorial

Resolution IV fractional factorial designs permit estimation of all main effects in the presence of two factor interactions which may not be estimable, For the factorial experiment, where , a lower bound on the number of runs required for a resolution IV design is Excepting designs for the 2n and 22 × 2s experiments, and two-factor designs that are actually resolution V, no series of designs attaining this bound are known. The construction method given in this paper yields resolution IV designs near the theoretical (and perhaps often unattainable) lower bound. For the 2m × 3n factorial the designs exceed the lower bound by 6 if n ≥ 3 by 4 if n = 2, and by 3 if n = 1. More generally, for the experiment, s1 < s2the designs exceed the lower bound by s2(s2-1) if n ≥ 3, by if n = 2, and by s2(s2-1) if n=1. In general the designs never exceed the lower bound by more than sk (sk-l).