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Optimal supersaturated designs for \(s^m\) factorials in \(N \not\equiv 0 \pmod s\) runs. (English) Zbl 1425.62105

Summary: Supersaturated designs (SSDs) offer apotentially useful way to investigate many factors with only a few experiments during the preliminary stages of experimentation. A popular measure to assess multilevel SSDs is the \(E({\chi}^2)\) criterion. The literature reports on SSDs have concentrated mainly on balanced designs. For \(s\)-level SSDs, the restriction of the number of runs \(N\) being only a multiple of \(s\) is really not required for the purpose of use of such designs. Just like when \(N\) is a multiple of \(s\) and the design ensures orthogonality of the factor effects with the mean effect, in the case of \(N\) not a multiple of \(s\), we ensure near orthogonality of each of the factors with the mean. In this article we consider \(s\)-level \(E({\chi}^2)\)-optimal designs for \(N \equiv n \pmod s\), \(0 \leq n \leq s - 1\). We give an explicit lower bound on \(E({\chi}^2)\). We give the structures of design matrices that attain the lower bounds. Some combinatorial methods for constructing \(E({\chi}^2)\)-optimal SSDs are provided.

MSC:

62K15 Factorial statistical designs
62K05 Optimal statistical designs
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