E(s2)-optimal Supersaturated Designs

Abstract

A popular measure to assess 2-level supersaturated designs is the E(s2) criterion. In this talk, we consider 2-level supersaturated designs with even as well as odd number of runs which have minimum E(s2). Improved or more explicit lower bounds on E(s2) are obtained. Similar bounds has recently been established by Ryan and Bulutoglu [J. Statist. Plann. Inference 137 (2007), 2250-2262] and Bulutoglu and Ryan [J. Statist. Plann. Inference 138 (2008), 1754-1762]. However, our analysis provides more details on precisely when an improvement is possible. For the even case, the equivalence of the bounds obtained by Butler, Mead, Eskridge and Gilmour [J. R. Statist. Soc. B 63(2001), 621-632] (in the cases where their result applies) and those obtained by Bulutoglu and Cheng [Ann. Statist. 32 (2004), 1662-1678] is established. Conditions for supersaturated designs which attain the lower bounds are given. Hadamard matrices and finite fields are used for constructing E(s2)-optimal supersaturated designs. The lower bound is improved when the number of factors is large, and designs attaining the improved bounds are constructed by using the complements of designs with small number of factors. We also give a method to construct E(s2)-optimal supersaturated designs with odd number of runs from E(s2)-optimal supersaturated designs with even number of runs by deleting a run.