Computer experiments with branching and nested factors are a common class of computer experiments, but it is challenging to construct designs for this type of experiments. In this paper, we define a special type of design called branching orthogonal Latin hypercube design (BOLHD). Such a design has an appealing structure, that is, no matter at each level of a branching factor or the level-combination of branching factors, the corresponding design points of nested factors form an orthogonal Latin hypercube design (OLHD). This structure makes it a good choice for designing computer experiments with branching and nested factors. We propose several deterministic construction methods when branching factors have the same number of levels. Based on sliced Latin hypercube designs (SLHDs), the proposed methods are easy to operate. Some construction results are tabulated for practical use.

中文翻译：

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具有分支和嵌套因子的正交设计

具有分支和嵌套因子的计算机实验是一类常见的计算机实验，但为此类实验构建设计具有挑战性。在本文中，我们定义了一种特殊类型的设计，称为分支正交拉丁超立方体设计 (BOLHD)。这样的设计有一个吸引人的结构，即无论在分支因子的每一层级还是分支因子的层级组合上，嵌套因子对应的设计点都形成了正交拉丁超立方设计（OLHD）。这种结构使其成为设计具有分支和嵌套因子的计算机实验的不错选择。当分支因子具有相同数量的级别时，我们提出了几种确定性构造方法。基于切片拉丁超立方体设计（SLHD），所提出的方法易于操作。