LINEAR PROGRAMMING BOUNDS FOR SPHERICAL (k, k)-DESIGNS

被引：1
|
作者：
Boyvalenkov, Peter G. [1 ,2 ]
机构：
[1] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev St,Bl 8, Sofia 1113, Bulgaria
[2] South Western Univ, Tech Fac, Blagoevgrad, Bulgaria
来源：
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2020年 / 73卷 / 08期
关键词：
spherical; (k; k)-designs; linear programming; DISTANCE; DESIGNS;
D O I：
10.7546/CRABS.2020.08.02
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We derive general linear programming bounds for spherical (k, k)-designs. This includes lower bounds for the minimum cardinality and lower and upper bounds for minimum and maximum energy, respectively. As applications we obtain a universal bound in the sense of Levenshtein for the minimum possible cardinality of a (k, k) design for fixed dimension and k and corresponding optimality result. We also discuss examples and possibilities for attaining the universal bound.
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页码：1051 / 1059
页数：9
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