Abstract Rotated sphere packing design is constructed by scaling, rotating and translating the lattice that has asymptotically lowest fill distance, its space-filling properties are very well. Currently, it can only be used for experimental design in hypercube. In this paper, we generalize the sphere packing design to simplex, which is the domain of experimental design with mixtures. In order to use the lattice method in simplex, a distance preserving transformation function is implemented to transform the simplex into the hyperplane, and then the iteration of rotating, scaling and disturbing is used to extract n lattice points as the design array. Some numerical comparisons between our method and several other popular methods are also provided. The results show that the designs generated by our algorithm are excellent according to the maximin distance criterion and its predictive ability is well. An additional searching method is also suggested to further improve the design.

中文翻译：

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用于混合物实验的球体填充设计

摘要 旋转球填充设计是通过缩放、旋转和平移具有渐近最小填充距离的点阵来构造的，其空间填充性能非常好。目前，它只能用于超立方体中的实验设计。在本文中，我们将球体填充设计推广到单纯形，这是混合实验设计的领域。为了在单纯形中使用格子法，实现了一个距离保持变换函数，将单纯形变换到超平面，然后通过旋转、缩放和扰动的迭代，提取出n个格点作为设计阵列。还提供了我们的方法与其他几种流行方法之间的一些数值比较。结果表明，根据最大最小距离准则，我们的算法生成的设计是优秀的，并且其预测能力良好。还建议使用额外的搜索方法来进一步改进设计。