Minimum aberration construction results for nonregular two‐level fractional factorial designs

Abstract

Nonregular two‐level fractional factorial designs are designs which cannot be specified in terms of a set of defining contrasts. The aliasing properties of nonregular designs can be compared by using a generalisation of the minimum aberration criterion called minimum G 2 ‐aberration. Until now, the only nontrivial designs that are known to have minimum G 2 ‐aberration are designs for n runs and m ≥ n −5 factors. In this paper, a number of construction results are presented which allow minimum G 2 ‐aberration designs to be found for many of the cases with n = 16, 24, 32, 48, 64 and 96 runs and m ≥ n /2−2 factors.