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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.

##### MSC:
 62K15 Factorial statistical designs