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Characterization of minimum aberration \(2^{n-k}\) designs in terms of their complementary designs. (English) Zbl 0867.62068

Summary: A general result is obtained that relates the word-length pattern of a \(2^{n-k}\) design to that of its complementary design. By applying this result and using group isomorphism, we are able to characterize minimum aberration \(2^{n-k}\) designs in terms of properties of their complementary designs. The approach is quite powerful for small values of \(2^{n-k}-n-1\). In particular, we obtain minimum aberration \(2^{n-k}\) designs with \(2^{n-k}-n-1=1\) to 11 for any \(n\) and \(k\).

MSC:

62K15 Factorial statistical designs
62K05 Optimal statistical designs
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