Chen, Hegang H.; Cheng, Ching-Shui Some results on \(2^{n - m}\) designs of resolution IV with (weak) minimum aberration. (English) Zbl 1369.62184 Ann. Stat. 37, No. 6A, 3600-3615 (2009). Summary: 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. 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