Computer experiments play a crucial role when physical experiments are expensive or difficult to be carried out. As a kind of designs for computer experiments, maximin distance designs have been widely studied. Many existing methods for obtaining maximin distance designs are based on stochastic algorithms, and these methods will be infeasible when the run size or number of factors is large. In this paper, we propose some deterministic construction methods for maximin $$L_2$$ L 2 -distance designs in two to five dimensions based on densest packings. The resulting designs have large $$L_2$$ L 2 -distances and are mirror-symmetric. Some of them have the same $$L_2$$ L 2 -distances as the existing optimal maximin distance designs, and some of the others are completely new. Especially, the resulting 2-dimensional designs possess a good projection property.

中文翻译：

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基于最密堆积的最大距离设计

当物理实验昂贵或难以进行时，计算机实验起着至关重要的作用。作为计算机实验的一种设计，最大最小距离设计已被广泛研究。许多现有的获得最大距离设计的方法都是基于随机算法的，当游程大小或因子数量很大时，这些方法将不可行。在本文中，我们提出了一些确定性构造方法，用于基于最密集堆积的两到五个维度的 maximin $$L_2$$ L 2 -距离设计。所得设计具有大$$L_2$$L 2 -距离并且是镜像对称的。其中一些具有与现有最优最大最小距离设计相同的 $$L_2$$ L 2 -距离，而其他一些则是全新的。尤其，