Cyclicly constructed E(s2)E(s2)-optimal supersaturated designs

Nguyen [1996. An algorithmic approach to constructing supersaturated designs. Technometrics 38, 69–73] and Tang and Wu [1997. E(s2)E(s2)-optimality of supersaturated designs. Statist. Sinica 7, 929–939] independently derived a lower bound for the E(s2)E(s2) value of an N run, m factor supersaturated design (SSD). This bound can be achieved only if m   is a multiple of N-1N-1 when N≡0(mod4) or if m   is an even multiple of N-1N-1 when N≡2(mod4). 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(s2)E(s2)-optimal SSD achieving the Nguyen–Tang–Wu bound with N   runs and t(N-1)t(N-1) factors when N≡0(mod4) and 2t(N-1)2t(N-1) factors when N≡2(mod4). This method is applied to the N=12,14,18,20,24,26,28,30,32,38,42,44,48,50,54N=12,14,18,20,24,26,28,30,32,38,42,44,48,50,54 cases.