D_4根系并非普遍最优
The D_4 root system is not universally optimal
摘要：
我们证明了D_4根系（等价于正则24-胞腔的顶点集）不是一个普适的最优球码。我们进一步推测，在S^3中不存在24点的通用最优球码，基于数值计算，表明S^3中由24点组成的每个5-设计都在D_4根系变形的3-参数族中（我们基于Sali的构造明确地描述了该族）。
英文摘要：
We prove that the D_4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S^3, based on numerical computations suggesting that every 5-design consisting of 24 points in S^3 is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the D_4 root system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
