On E(s2)-optimal supersaturated designs

A popular measure to assess 2-level supersaturated designs is the E(s2) criterion. In this paper, improved lower bounds on E(s2) are obtained. The same improvement has recently been established by Ryan and Bulutoglu [2007. E(s2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250-2262]. However, our analysis provides more details on precisely when an improvement is possible, which is lacking in Ryan and Bulutoglu [2007. E(s2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250-2262]. The equivalence of the bounds obtained by Butler et al. [2001. A general method of constructing E(s2)-optimal supersaturated designs. J. Roy. Statist. Soc. B 63, 621-632] (in the cases where their result applies) and those obtained by Bulutoglu and Cheng [2004. Construction of E(s2)-optimal supersaturated designs. Ann. Statist. 32, 1662-1678] is established. We also give two simple methods of constructing E(s2)-optimal designs.