E(s2)-optimal supersaturated designs with good minimax properties when N is odd

An improved E(s2) lower bound is derived for two-level supersaturated designs (SSDs) with an odd number of runs. The new bound is used to prove E(s2)-optimality of SSDs with N=5, 7, 9, 11, 13, 15, and 17 runs found via the NOAp exchange algorithms. Tailored to find cyclically generated E(s2)-optimal SSDs, the CNOAp exchange algorithms are introduced; search results are compared to related literature. Exchange algorithms that promote the finding of SSDs which are simultaneously optimal (or near optimal) wrt E(s2) and minimax criteria are discussed. Proving the minimax optimality of E(s2)-optimal SSDs is also discussed.