Cyclicly constructed E(s2)-optimal supersaturated designs

Nguyen [1996. An algorithmic approach to constructing supersaturated designs. Technometrics 38, 69-73] and Tang and Wu [1997. E(s(2))-optimality of supersaturated designs. Statist. Sinica 7, 929-939] independently derived a lower bound for the E(s(2)) value of an N run, m factor supersaturated design (SSD). This bound can be achieved only if m is a multiple of N - 1 when N equivalent to 0 (mod 4) or if m is an even multiple of N - 1 when N = 2 (mod 4). One important question is whether Nguyen-Tang-Wu bound can be achieved in all of these cases. In this paper, based on a construction method by Bulutoglu and Cheng (2004), we present a theoretical method for finding as many positive integers t as possible such that there is an E(s(2))-optimal SSD achieving the Nguyen-Tang-Wu bound with N runs and t (N - 1) factors when N equivalent to 0 (mod 4) and 2t (N - 1) factors when N equivalent to 2 (mod 4). This method is applied to the N = 12, 14, 18, 20, 24, 26, 28, 30, 32, 38, 42, 44, 48, 50, 54 cases. (c) 2006 Elsevier B.V. All rights reserved.