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Enumerating nonisomorphic orthogonal arrays is an important, yet verydifficult, problem. Although orthogonal arrays with a specified set ofparameters have been enumerated in a number of cases, general results areextremely rare. In this paper, we provide a complete solution to enumeratingnonisomorphic two-level orthogonal arrays of strength $d$ with $d+2$constraints for any $d$ and any run size $n=\lambda2^d$. Our results not onlygive the number of nonisomorphic orthogonal arrays for given $d$ and $n$, butalso provide a systematic way of explicitly constructing these arrays. Ourapproach to the problem is to make use of the recently developed theory of$J$-characteristics for fractional factorial designs. Besides the generaltheoretical results, the paper presents some results from applications of thetheory to orthogonal arrays of strength two, three and four.

Complete enumeration of two-Level orthogonal arrays of strength $d$ with $d+2$ constraints