具有$d+2$约束的二级强度正交表PDMATHAAB的完备enumeration
Complete enumeration of two-Level orthogonal arrays of strength $d$ with $d+2$ constraints
摘要：
枚举非同构正交表是一个重要而又困难的问题。虽然在许多情况下已经列举了具有指定参数集的正交表，但一般结果是极其罕见的。在本文中，我们提供了一个完整的解决方案，枚举非同构的两级正交表的强度$d$与$d+2$的限制，任何$d$和任何运行大小$n=\lambda2^d$。我们的结果不仅给出了给定$d$和$n$的非同构正交表的个数，而且提供了一种显式构造这些正交表的系统方法.我们解决这个问题的方法是利用最近发展起来的$J$ -特征部分析因设计的理论。除了一般的理论结果外，本文还介绍了该理论在强度为2、3和4的正交表中的应用结果。
英文摘要：
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.
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