Summary Space-filling designs are widely used in computer experiments. Inspired by the stratified orthogonality of strong orthogonal arrays, we propose a criterion of minimum aberration-type for assessing the space-filling properties of designs based on design stratification properties on various grids. A space-filling hierarchy principle is proposed as a basic assumption of the criterion. The new criterion provides a systematic way of classifying and ranking space-filling designs, including various types of strong orthogonal arrays and Latin hypercube designs. Theoretical results and examples are presented to show that strong orthogonal arrays of maximum strength are favourable under the proposed criterion. For strong orthogonal arrays of the same strength, the space-filling criterion can further rank them based on their space-filling patterns.

中文翻译：

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选择空间填充设计的最小像差类型标准

总结 空间填充设计广泛用于计算机实验。受强正交阵列分层正交性的启发，我们提出了一种最小像差类型的标准，用于基于各种网格上的设计分层特性来评估设计的空间填充特性。提出了空间填充层次原则作为该准则的基本假设。新标准提供了一种对空间填充设计进行分类和排序的系统方法，包括各种类型的强正交阵列和拉丁超立方体设计。理论结果和例子表明，在所提出的标准下，最大强度的强正交阵列是有利的。对于相同强度的强正交阵列，空间填充标准可以根据它们的空间填充模式进一步对它们进行排名。