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October 2021 Construction of mixed orthogonal arrays with high strength
Shanqi Pang, Jing Wang, Dennis K. J. Lin, Min-Qian Liu
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Ann. Statist. 49(5): 2870-2884 (October 2021). DOI: 10.1214/21-AOS2063


A considerable portion of the work on mixed orthogonal arrays applies specifically to arrays of strength 2. Although strength t=2 is arguably the most important case for statistical applications, there is an urgent need for better methods for t3. However, the knowledge on the existence of arrays for t3 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 t3. 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.

Funding Statement

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.


Download Citation

Shanqi Pang. Jing Wang. Dennis K. J. Lin. Min-Qian Liu. "Construction of mixed orthogonal arrays with high strength." Ann. Statist. 49 (5) 2870 - 2884, October 2021.


Received: 1 May 2019; Revised: 1 January 2021; Published: October 2021
First available in Project Euclid: 12 November 2021

Digital Object Identifier: 10.1214/21-AOS2063

Primary: 62K15
Secondary: 05B15

Keywords: High strength orthogonal arrays , Kronecker product , Orthogonal partitions

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 5 • October 2021
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