Some results on 2n−m designs of resolution IV with (weak) minimum aberration

Abstract

It is known that all resolution IV regular 2^n−m designs of run size N=2^n−m where 5N/16<n<N/2 must be projections of the maximal even design with N/2 factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even 2^n−m design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration 2^n−m designs of resolution IV and the structures of their complementary designs. Based on these results, several families of minimum aberration 2^n−m designs of resolution IV are constructed.