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A note on the lower bounds on maximum number of clear two-factor interactions for \((2^{m - p}_{III})\) and \((2^{m - p}_{IV})\) designs. (English) Zbl 1093.62073
Summary: The clear effects criterion is one of the most important rules for selecting \(2^{m - p}\) designs, and it is valuable to know the maximum number of clear two-factor interactions in \(2^{m - p}\) designs. This article provides lower bounds on the maximum number of clear two-factor interactions for \(2^{m-p}_{III}\) and \(2^{m-p}_{IV}\) designs by constructing specific designs, respectively. The lower bounds improve the ones given by B. Tang et al. [Can. J. Stat. 30, No. 1, 127–136 (2002; Zbl 0999.62059)] and the construction methods perform quite well.

MSC:
62K15 Factorial statistical designs
62K05 Optimal statistical designs
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