Complete enumeration of two-level orthogonal arrays of strength \(d\) with \(d+2\) constraints. (English) Zbl 1117.62077

Stufken, John; Tang, Boxin

Ann. Stat. 35, No. 2, 793-814 (2007).

Summary: 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. 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 \(n=\lambda2^d\). 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.

MSC:

62K15	Factorial statistical designs
05B15	Orthogonal arrays, Latin squares, Room squares
05A99	Enumerative combinatorics

Keywords:

design resolution; fractional factorial design; Hadamard matrix; Hadamard transform; indicator function; isomorphism; \(J\)-characteristic; minimum aberration

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