Optimal Supersaturated Designs for sm Factorials in N ≢ 0 (mod s) Runs

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(χ2) 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(χ2)-optimal designs for N ≡ n (mod s), 0 ≤ n ≤ s − 1. We give an explicit lower bound on E(χ2). We give the structures of design matrices that attain the lower bounds. Some combinatorial methods for constructing E(χ2)-optimal SSDs are provided.

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