Characterization of minimum aberration mixed factorials in terms of consulting designs

In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain combinatorial identities that relate the wordlength pattern of a regular mixed factorial design to that of its consulting design. According to these identities, we furthermore establish the general and unified rules for identifying minimum aberration mixed factorial designs through their consulting designs. It is an improvement and generalization of the results in Mukerjee and Wu (2001).