Distributing points on a (possibly high-dimensional) sphere with minimal energy is a long-standing problem in and outside the field of mathematics. This paper considers a novel energy function that arises naturally from statistics and combinatorial optimization, and studies its theoretical properties. Our result solves both the exact optimal spherical point configurations in certain cases and the minimal energy asymptotics under general assumptions. Connections between our results and the L1-Principle Component Analysis and Quasi-Monte Carlo methods are also discussed.

翻译：将最小能量(可能高维)球体的点数分布在数学领域(可能是高维的)球体上是一个长期存在的问题。 本文认为,从统计和组合优化中自然产生一种新的能源功能,并研究其理论属性。 我们的结果解决了某些情况下精确的最佳球点配置和一般假设下的最低能量杂交。 还讨论了我们的结果与L1-原则组成部分分析和Qaasi- Monte Carlo方法之间的联系。