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摘要翻译：
非同构正交数组的枚举是一个重要而又非常困难的问题。尽管具有指定参数集的正交数组已经在许多情况下被枚举过，但一般结果极其罕见。本文给出了任意$d$和任意运行大小$n=\lambda2^d$的具有$d+2$约束的非同构两级强度正交数组的一个完整的枚举方法。我们的结果不仅给出了给定$d$和$n$的非同构正交数组的个数，而且提供了显式构造这些数组的系统方法。我们解决这个问题的方法是利用最近发展起来的分数阶乘设计的$J$-特征理论。除了一般的理论结果外，本文还给出了将该理论应用于二、三、四强度正交阵的一些结果。
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英文标题：
《Complete enumeration of two-Level orthogonal arrays of strength $d$ with
$d+2$ constraints》
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作者：
John Stufken, Boxin Tang
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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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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PDF链接：
https://arxiv.org/pdf/708.1908
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