Linear Programming Bounds for Covering Radius of Spherical Designs

被引：0
作者：
Peter Boyvalenkov
Maya Stoyanova
机构：
[1] Bulgarian Academy of Sciences,Institute of Mathematics and Informatics
[2] Sofia University,Faculty of Mathematics and Informatics
来源：
Results in Mathematics | 2021年 / 76卷
关键词：
Spherical designs; covering radius; linear programming; 05B30;
D O I：
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摘要：
We apply polynomial techniques (i.e., techniques which invole polynomials) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower bounds due to Fazekas and Levenshtein and propose new upper bounds. Our approach to the lower bounds involves certain signed measures whose corresponding series of orthogonal polynomials are positive definite up to a certain (appropriate) degree. The upper bounds are based on a geometric observation and more or less standard in the field linear programming techniques.
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