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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.

MSC:
62K15 Factorial statistical designs
62Q05 Statistical tables
62K05 Optimal statistical designs
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