Non-Uniqueness of E(s2)-Optimal Supersaturated Designs for N ≡ 2 (mod 4) Runs with Application to the Case N = 10 Runs

In factor screening experiments with limited resources, it is common for practitioners to cut down the number of runs N and choose a supersaturated design for the experiment. In the past two decades, E(s2)-optimality has been one of the most important criteria used to choose a supersaturated design. We show that the definition E(s2)-optimal supersaturated designs X for N ≡ 2 (mod 4) runs and m ≥ N factors are not unique by showing that XX⊤ allows for multiple non-isomorphic possibilities for most values of m. For N = 10 and 12 ≤ m ≤ 114 we list all possible E(s2)-optimal designs.