  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 $n=\lambda2^d$. 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.
