Space-filling designs with low-dimensional stratifications are desirable choices for computer experiments. In addition, column orthogonality is an important property of designs for such experiments, because it allows the estimates of the main effects in linear models to be uncorrelated with each other. However, few works have examined space-filling designs with both properties. This paper proposes a new class of designs called strong group-orthogonal arrays, the columns of which can be partitioned into groups, with the columns from different groups being column orthogonal and enjoying attractive low-dimensional stratifications. In addition, the overall arrays collapse to fully orthogonal arrays that accommodate large numbers of factors, making them particularly suitable for computer experiments. Methods for constructing this class of arrays based on both regular and nonregular designs are proposed. Difference schemes play a key role in the construction. Lastly, the proposed methods are easy to implement.

中文翻译：

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强群正交阵列的构建

具有低维分层的空间填充设计是计算机实验的理想选择。此外，列正交性是此类实验设计的一个重要属性，因为它允许线性模型中主效应的估计彼此不相关。然而，很少有作品研究具有这两种特性的空间填充设计。本文提出了一类新的设计，称为强组正交阵列，其列可以划分为组，来自不同组的列是列正交的，并且具有有吸引力的低维分层。此外，整个阵列折叠成完全正交的阵列，可容纳大量因子，使其特别适合计算机实验。提出了基于规则和非常规设计的此类数组的构造方法。差异方案在构建中起着关键作用。最后，所提出的方法易于实现。