Constructing definitive screening designs using cyclic generators

Jones and Nachtsheim (2011) propose a new class of computer-generated three-level screening designs called definitive screening designs (DSDs). These designs provide estimates of main effects that are unbiased by any second-order effect and require only one more than twice the number of factors. Stylianou (2011) and Xiao et al. (2012) suggest the construction of these designs using conference matrices. The resulting DSD is always global optimum. This method is only applicable when the number of factors is even. This article introduces an algorithm for constructing DSDs for both even and odd numbers of factors using cyclic generators. We show that our algorithm can construct designs that are more efficient than those of Jones and Nachtsheim (2011) and that it can construct much larger designs.