Construction of two-level nonregular designs of strength three with large run sizes

Two-level orthogonal arrays of strength 3 permit the study of the main effects and the two-factor interactions of the experimental factors. These arrays are classified into regular and nonregular designs. Good regular designs are available in the literature for large run sizes that are a power of 2. In contrast, good nonregular designs, which have run sizes that are multiples of 8 and are more exible alternatives to regular designs, are not available for large numbers of runs because their construction is challenging. The contribution of this paper is a collection of strength-3 nonregular designs with large run sizes that, to the best of our knowledge, have not been explored before in the design literature. Using theoretical results and algorithmic approaches, we generate nonregular designs with up to 1280 runs. Our designs fill the gaps between the available strength-3 designs with large run sizes and outperform comparably-sized regular designs in terms of the aliasing among the two-factor interactions. We show the applicability of the new collection of strength-3 designs using a drug combination experiment.