Es^2-optimal Supersaturated Designs for 2-level Factors

Abstract

Booth and Cox (1962) pioneered the notion of E(s^2) criterion for constructing two- level supersaturated designs. Nguyen (1996) and Tang and Wu (1997) independently obtained a lower bound for E(s^2). This lower bound can be achieved only when m is a multiple of (n ?€“ 1) where m is the number of factors and n is the number of runs. Bulutoglu and Cheng (2004) described a method that uses difference families to construct designs that satisfy this lower bound. They also derived better lower bounds for the case where the Nguyen, Tang-Wu bound is not achievable. Their bounds cover more cases than a bound obtained by Butler, Mead, Eskridge and Gilmour (2001). The purpose of the present talk is to give the notion of supersaturated design and also to give the flavor of E (s^2) optimality and the corresponding bounds for 2- level factors.