论文标题
部分可观测时空混沌系统的无模型预测
Packing and covering in higher dimensions
论文作者
论文摘要
目前的工作调查了$ n $维空间中的问题，其中$ n $大。数量的几何形状激发了高维度的包装和覆盖研究的早期发展。随后的结果，例如发现水ech晶格和线性编程结合，这些结合在尺寸8和24中最新的球体堆积问题解决方案中受到了最终影响，受到编码理论的影响。在提到有关存在经济包装和覆盖物的已知结果之后，我们讨论了不同的方法，这些方法产生了填料一致球密度的上限。我们总结了一般凸形体的填料密度的上限的少数结果。纸张关闭了有关最佳布置结构的一些评论。
The present work surveys problems in $n$-dimensional space with $n$ large. Early development in the study of packing and covering in high dimensions was motivated by the geometry of numbers. Subsequent results, such as the discovery of the Leech lattice and the linear programming bound, which culminated in the recent solution of the sphere packing problem in dimensions 8 and 24, were influenced by coding theory. After mentioning the known results concerning existence of economical packings and coverings we discuss the different methods yielding upper bounds for the density of packing congruent balls. We summarize the few results on upper bounds for the packing density of general convex bodies. The paper closes with some remarks on the structure of optimal arrangements.
