E(s2)-optimal supersaturated designs with odd number of runs

A popular measure to assess 2-level supersaturated designs with even number of runs is the E(s2) criterion. In this paper, we consider 2-level supersaturated designs with odd number of runs which have minimum E(s2). We give a more explicit lower bound on E(s2) than Bulutoglu and Ryan (2008). Conditions of supersaturated designs which attain the lower bounds are given. E(s2)-optimal supersaturated designs attaining the lower bounds are listed for n=5 and 7. 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.