The D 4 Root System Is Not Universally Optimal
The D 4 Root System Is Not Universally Optimal
复制标题
D 4 根系统并非普遍最优
DOI：
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发表时间：
2006
影响因子：
0.5
通讯作者：
Abhinav Kumar
中科院分区：
文献类型：
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作者：
Henry Cohn;J. Conway;N. Elkies;Abhinav Kumar
我们证明 D 4 根系统（相当于常规 24 单元的顶点集）不是通用最优球形码。我们进一步推测，S 3 中不存在普遍最优的 24 点球形代码，基于数值计算表明，S 3 中包含 24 个点的每个 5 设计都属于 D 4 根系变形的 3 参数族（我们基于 Sali 的构造明确描述了该族）。
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.