Sn− m Designs containing clear main effects or clear two-factor interactions

Abstract

For a fixed number of runs, when can designs have clear main effects or clear two-factor interactions (in brief, 2fi's)? This paper gives the maximum value of n in s n− m designs containing clear main effects or clear 2fi's, where s is any prime or prime power. It is a generalization of the related results in Chen and Hedayat (J. Statist. Plann. Inference 75 (1998) 147–158) for two-level designs. It is further concluded that the weak minimum aberration designs have a maximum number of clear main effects for two-level designs. A collection of designs containing most clear main effects or clear 2fi's for 16, 32, 27, and 81 runs is given.