A considerable portion of the work on mixed orthogonal arrays applies specifically to arrays of strength 2. Although strength is arguably the most important case for statistical applications, there is an urgent need for better methods for . However, the knowledge on the existence of arrays for 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 . 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.
Shanqi Pang was supported by NNSF of China Grant 11971004.
Jing Wang was supported by NNSF of China Grant 11971318 and by Shanghai Rising-Star Program 20QA1407500.
Dennis K. J. Lin was supported by NSF Grant DMS-18-102925.
Min-Qian Liu was supported by NNSF of China Grant 11771220 and by the National Ten Thousand Talents Program.
The authors thank the Co-Editors, the Associate Editor and three referees for their valuable and constructive comments which have led to significant improvements in the paper.
Shanqi Pang is the corresponding author.
"Construction of mixed orthogonal arrays with high strength." Ann. Statist. 49 (5) 2870 - 2884, October 2021. https://doi.org/10.1214/21-AOS2063