Recently, the construction of nested or sliced Latin hypercube designs (LHDs) has received notable interest for planning computer experiments with special combinational structures. In this paper, we propose an approach to constructing nested and/or sliced LHDs by using small LHDs and structural vectors/matrices. This method is easy to implement, and can generate nested and sliced LHDs through a unified algorithm. Moreover, an algorithm for improving the space-filling properties of the resulting designs is developed, and under some control the orthogonality of the constructed designs are attainable. Some examples are provided for illustrating the proposed algorithms.

中文翻译：

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构建具有嵌套和切片结构的拉丁超立方体设计

最近，嵌套或切片拉丁超立方体设计 (LHD) 的构建在规划具有特殊组合结构的计算机实验方面引起了极大的兴趣。在本文中，我们提出了一种通过使用小型 LHD 和结构向量/矩阵来构建嵌套和/或切片 LHD 的方法。该方法易于实现，可以通过统一的算法生成嵌套和切片的LHD。此外，还开发了一种算法，用于改进最终设计的空间填充特性，并且在某些控制下，可以实现所构造设计的正交性。提供了一些示例来说明所提出的算法。