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.