Minimum aberration blocking of regular mixed factorial designs

It is known by Zhang and Park (J. Statist. Plann. Inference 91 (2000) 107) that there are no minimum aberration (MA) designs with respect to both treatments and blocks for blocked regular mixed-level factorial designs. So it should be compromised between the block wordlength pattern and treatment wordlength pattern. Two methods are considered in this article. The first is MA blocking scheme of an MA design. The other is to combine the components of the two wordlength pattern vectors into one combined wordlength pattern according to the modified hierarchical assumptions and an appropriate ordering of the numbers of alias or confounding relations. The relationship between the two types of optimal blocked designs is investigated. A complete catalogue of optimal blocked regular mixed factorial designs of the above two types with 16 or 32 runs is given.