Clear two-factor interactions and minimum aberration

Wu and Hamada recommend selecting resolution IV designs with the maximum number of clear two-factor interactions (2FIs), called MaxC2 designs. In this paper, we develop a method by using graphical representations, combinatorial and group-theoretic arguments to prove if a given design is a MaxC2 design. In particular, we show that all known minimum aberration designs with resolution IV are MaxC2 designs (except in six cases) and that the second 2⁹⁻⁴, 2¹³⁻⁷, 2¹⁶⁻¹⁰ and 2¹⁷⁻¹¹ designs given in Wu and Hamada are MaxC2 designs. The method also enables us to identify new MaxC2 designs that are too large to be verified by computer search.