In this paper, we study some cube packing problems. In particular, we are interested in compact subsets of ${\mathbb{R}}^n,n⩾2$, which contain boundaries of cubes with all side lengths in (0,1). We show here that such sets must have lower box dimension at least $n-0.5$, and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper.

中文翻译：

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欧盟地区的多维数据集包装

在本文中，我们研究了一些立方体包装问题。特别是，我们对...的紧凑子集感兴趣${\mathbb{[R}}^{ñ}，ñ⩾2$，其中包含所有边长在（0,1）中的立方体边界。我们在这里表明，这样的集合至少必须具有较小的盒子尺寸$ñ-0.5$，我们还将提供一些清晰的示例。在这里，我们还表明，从精确的意义上讲，这样的集合通常必须很大，本文也对此进行了介绍。