Construction of mixed orthogonal arrays with high strength

Abstract

A considerable portion of the work on mixed orthogonal arrays applies specifically to arrays of strength 2. Although strength $\mathit{t}=2$ is arguably the most important case for statistical applications, there is an urgent need for better methods for $\mathit{t}\ge 3$. However, the knowledge on the existence of arrays for $\mathit{t}\ge 3$ is rather limited. In this paper, new construction methods for symmetric and asymmetric orthogonal arrays (OAs) with high strength are proposed by using lower strength orthogonal partitions of spaces and OAs. A positive answer is provided to the open problem in Hedayat, Sloane and Stufken (Orthogonal Arrays: Theory and Applications (1999) Springer) on developing better methods and tools for the construction of mixed orthogonal arrays with strength $\mathit{t}\ge 3$. Not only are the methods straightforward, but also they are useful for constructing symmetric or asymmetric OAs of arbitrary strengths, numbers of levels and various sizes. The constructed OAs can be utilized to generate more OAs. The resulting OAs have a high degree of flexibility and many other desirable properties. Some selective OAs are tabulated for practical uses.