Abstract
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.
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