An algorithm for constructing mixed-level kk-circulant supersaturated designs

Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Recently, Chen and Liu [Chen, J., Liu, M.Q., 2008a. Optimal mixed-level kk-circulant supersaturated designs. J. Statist. Plann. Inference 138, 4151–4157] explored the construction of E(fNOD)-optimal mixed-level SSDs using kk-cyclic generators. As an extension, this paper further studies how to construct optimal mixed-level kk-circulant SSDs under the χ2(D)χ2(D) criterion. A sufficient condition under which the generator vector produces a χ2(D)χ2(D)-optimal SSD is obtained, and some other properties of the resulting SSDs are investigated. Note that, the construction of optimal mixed-level kk-circulant SSDs under the χ2(D)χ2(D) criterion is much more complicated than that under E(fNOD). Hence, an algorithm for finding generators of (nearly) χ2(D)χ2(D)-optimal designs is provided, and many (nearly) χ2(D)χ2(D)-optimal mixed-level SSDs are then constructed.