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Intelligent search for \(2^{13-6}\) and \(2^{14-7}\) minimum aberration designs. (English) Zbl 0916.62056
Summary: Among all \(2^{n-k}\) regular fractional factorial designs, minimum aberration designs are often preferred. When \(2^{n-k}\) (the run-size) is no more than 64, most (possibly all) minimum aberration designs have been found. When \(2^{n-k}=128\), the search for minimum aberration designs becomes very hard. The results in J. Chen and C. F. J. Wu [Ann. Statist. 19, No. 2, 1028-1041 (1991; Zbl 0725.62068)] and J. Chen [ibid. 20, No. 4, 2124-2141 (1992; Zbl 0770.62063)] include all 128-run minimum aberration designs with \(k\leq 5\). When \(n\) is close to \(2^{n-k}\), B. Tang and C. F. J. Wu [ibid. 24, No. 6, 2549-2559 (1996; Zbl 0867.62068)] also obtain some minimum aberration designs. We search for 128-run minimum aberration designs with \(k=6\) and \(k=7\). By combining theoretical understanding with intelligent computer search, both cases are solved.

62K15 Factorial statistical designs