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\(s^{n-m}\) designs containing clear main effects or clear two-factor interactions. (English) Zbl 1062.62143
Summary: For a fixed number of runs, when can designs have clear main effects or clear two-factor interactions (in brief, 2fi’s)? This paper gives the maximum value of \(n\) in \(s^{n-m}\) designs containing clear main effects or clear 2fi’s, where \(s\) is any prime or prime power. It is a generalization of the related results of H. Chen and A. S. Hedayat [J. Stat. Plann. Inference 75, 147–158 (1998; Zbl 0938.62081)] for two-level designs. It is further concluded that the weak minimum aberration designs have a maximum number of clear main effects for two-level designs. A collection of designs containing most clear main effects or clear 2fi’s for 16, 32, 27, and 81 runs is given.

62K15 Factorial statistical designs
62Q05 Statistical tables
62K05 Optimal statistical designs
Full Text: DOI
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