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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.

62K15 Factorial statistical designs
62K05 Optimal statistical designs
Full Text: DOI
[1] DOI: 10.2307/1266725 · doi:10.2307/1266725
[2] DOI: 10.1016/S0378-3758(98)00122-0 · Zbl 0938.62081 · doi:10.1016/S0378-3758(98)00122-0
[3] DOI: 10.2307/1403599 · Zbl 0768.62058 · doi:10.2307/1403599
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[10] DOI: 10.1360/04ys0165 · doi:10.1360/04ys0165
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