A Note on Dominating Fractional Factorial Two-Level Designs With Clear Two-Factor Interactions

This note builds on results from Wu, Mee and Tang‘s (2012) article (henceforth WMT) on admissible fractional factorial two-level designs, specifically concentrating on the “dominating designs” that have been introduced but not further pursued in WMT. WMT’s work has been used for increasing the efficiency of the author’s graph-based algorithm for creation of minimum aberration designs that keep a requirement set of two-factor interactions clear (Grömping 2012, implemented in free open source software): That algorithm originally searched aberration-sorted complete catalogues of non-isomorphic resolution IV designs; according to WMT’s proposal, it suffices to search the dominating designs. For implementing this reduction of search space, aberration-sorted catalogues of dominating resolution IV regular fractional factorial two-level designs with up to 128 runs were created; this was achieved with the help of a recent subgraph isomorphism algorithm (Solnon 2010) that proved to be particularly efficient for this search task. The supplementary material provides the code used for identifying the dominating designs and ASCII files with the design generators for all resolution IV and higher dominating designs in 64 and 128 runs.