On kissing numbers and spherical codes in high dimensions

被引：19
作者：
Jenssen, Matthew [1 ]
Joos, Felix [2 ]
Perkins, Will [2 ]
机构：
[1] Univ Oxford, Oxford, England
[2] Univ Birmingham, Birmingham, W Midlands, England
来源：
ADVANCES IN MATHEMATICS | 2018年 / 335卷
基金：
英国工程与自然科学研究理事会;
关键词：
Kissing numbers; Spherical codes; High dimensional geometry; BOUNDS; ERROR;
D O I：
10.1016/j.aim.2018.07.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a lower bound of Omega(d(3/2) . (2/root 3)d) on the kissing number in dimension d. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in the dimension. We obtain a similar linear factor improvement to the best known lower bound on the maximal size of a spherical code of acute angle theta in high dimensions. (C) 2018 Elsevier Inc. All rights reserved.
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页码：307 / 321
页数：15
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