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April 2007 Complete enumeration of two-Level orthogonal arrays of strength d with d + 2 constraints
John Stufken, Boxin Tang
Ann. Statist. 35(2): 793-814 (April 2007). DOI: 10.1214/009053606000001325


Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d+2 constraints for any d and any run size n=λ2d. Our results not only give the number of nonisomorphic orthogonal arrays for given d and n, but also provide a systematic way of explicitly constructing these arrays. Our approach to the problem is to make use of the recently developed theory of J-characteristics for fractional factorial designs. Besides the general theoretical results, the paper presents some results from applications of the theory to orthogonal arrays of strength two, three and four.


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John Stufken. Boxin Tang. "Complete enumeration of two-Level orthogonal arrays of strength d with d + 2 constraints." Ann. Statist. 35 (2) 793 - 814, April 2007.


Published: April 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1117.62077
MathSciNet: MR2336869
Digital Object Identifier: 10.1214/009053606000001325

Primary: 62K15

Keywords: design resolution , Fractional factorial design , Hadamard matrix , Hadamard transform , Indicator function , isomorphism , J-characteristic , minimum aberration

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 2 • April 2007
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