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

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 G2‐aberration. Until now, the only nontrivial designs that are known to have minimum G2‐aberration are designs for n runs and m ≥ n−5 factors. In this paper, a number of construction results are presented which allow minimum G2‐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.