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February 2020 Construction results for strong orthogonal arrays of strength three
Chenlu Shi, Boxin Tang
Bernoulli 26(1): 418-431 (February 2020). DOI: 10.3150/19-BEJ1130


Strong orthogonal arrays were recently introduced as a class of space-filling designs for computer experiments. The most attractive are those of strength three for their economical run sizes. Although the existence of strong orthogonal arrays of strength three has been completely characterized, the construction of these arrays has not been explored. In this paper, we provide a systematic and comprehensive study on the construction of these arrays, with the aim at better space-filling properties. Besides various characterizing results, three families of strength-three strong orthogonal arrays are presented. One of these families deserves special mention, as the arrays in this family enjoy almost all of the space-filling properties of strength-four strong orthogonal arrays, and do so with much more economical run sizes than the latter. The theory of maximal designs and their doubling constructions plays a crucial role in many of theoretical developments.


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Chenlu Shi. Boxin Tang. "Construction results for strong orthogonal arrays of strength three." Bernoulli 26 (1) 418 - 431, February 2020.


Received: 1 October 2018; Revised: 1 March 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140504
MathSciNet: MR4036039
Digital Object Identifier: 10.3150/19-BEJ1130

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability


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Vol.26 • No. 1 • February 2020
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