On the Enumeration of math formula-Optimal and Minimax-Optimal k-Circulant Supersaturated Designs

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Abstract

In recent years, several methods have been proposed for constructing math formula-optimal and minimax-optimal supersaturated designs (SSDs). However, until now the enumeration problem of such designs has not been yet considered. In this paper, math formula-optimal and minimax-optimal k-circulant SSDs with math formula 6, 10, 14, 18, 22, and 26 runs, math formula factors and math formula are enumerated in a computer search. We have also enumerated all math formula-optimal and minimax-optimal k-circulant SSDs with math formula (mod 4) and math formula. The computer search utilizes the fact that theses designs are equivalent to certain 1-rotational resolvable balanced incomplete block designs. Combinatorial properties of these resolvable designs are used to restrict the search space.

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