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

It is known that all resolution IV regular 2n.m designs of run size N=2n.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 2n.m design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration 2n.m designs of resolution IV and the structures of their complementary designs. Based on these results, several families of minimum aberration 2n.m designs of resolution IV are constructed.