Grid representations for 2(IV)(m-(m-k)) join designs containing maximum number of clear two-factor interactions

摘要

This paper shows that the join designs [Butler, N.A., 2005. Classification of efficient two-level fractional factorial design of resolution IV or more. J. Statist. Plann. Inference 131, 145 - 159] include all 2(IV)(m - (m - k)) designs with the maximum number of clear two-factor interactions (2FIs) for k = 5, 6, 7. The designs are shown to have concise grid representations which provide simple interpretations of the 2FIs in a 2(IV)(m - (m - k)) design. In addition, a better upper bound on the maximum number of clear 2FIs in a 2(IV)(m - (m - k)) design than the one obtained by Tang et al. [2002. Bounds of the maximum members of clear factor interactions for 2(m - p) designs of resolution III and IV. Canad. J. Statist. 30, 127 - 136] is given.