Enumeration and evaluation of orthogonal three-level designs with small number of runs for definitive screening

A class of three-level designs for definitive screening was introduced by Jones and Nachtsheim (2011) and has been extensively studied because of its attractive properties for factor screening. The so-called definitive screening designs (DSDs) have columns with three levels and possess a fold-over structure which guarantees favorable properties under a full second-order linear model. The original DSDs have one center point, a total of three zeros per column, and study q factors in n=2q+1 runs. In recent progress on this field, new classes of three-level designs that attain the attractive properties of the original DSDs have been proposed, where the number of zeros per column can be greater than three, and the number of factors under study with the use of n=2q+1 runs can be less than q. So far, lists of non isomorphic n×q orthogonal three-level designs for definitive screening with n≤49 runs, n≡ 1 mod 4, three zeros per column and q≤(n−1)/2 columns have been established. In this article, we construct lists of non isomorphic orthogonal three-level designs for definitive screening that have three, five, and seven zeros per column for n≤33 runs, n odd. The constructed designs are evaluated using well-known criteria, and best designs are given for every run order.