New bounds for spherical two-distance sets

Alexander Barg; Wei Hsuan Yu

doi:10.1080/10586458.2013.767725

New bounds for spherical two-distance sets

Alexander Barg, Wei Hsuan Yu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

A spherical two-distance set is a finite collection of unit vectors in ℝⁿ such that the distance between two distinct vectors assumes one of only two values. We use the semidefinite programming method to compute improved estimates of the maximum size of spherical two-distance sets. Exact answers are found for dimensions n = 23 and 40 ≤ n ≤ 93 (n ≠ 46, 78), where previous results gave divergent bounds.

Original language	English
Pages (from-to)	187-194
Number of pages	8
Journal	Experimental Mathematics
Volume	22
Issue number	2
DOIs	https://doi.org/10.1080/10586458.2013.767725
State	Published - 3 Apr 2013

Keywords

Positive definite matrices
Semidefinite programming
Two-distance sets

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10.1080/10586458.2013.767725

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keywords = "Positive definite matrices, Semidefinite programming, Two-distance sets",

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note = "Funding Information: We are grateful to Chao-Wei Chen and Johan L{\"o}fberg for their significant help with the Matlab implementation. Research supported in part by NSF grants DMS1101697, CCF0916919, and CCF1217894, and NSA grant H78230-12-1-0260.",

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AU - Yu, Wei Hsuan

N1 - Funding Information: We are grateful to Chao-Wei Chen and Johan Löfberg for their significant help with the Matlab implementation. Research supported in part by NSF grants DMS1101697, CCF0916919, and CCF1217894, and NSA grant H78230-12-1-0260.

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N2 - A spherical two-distance set is a finite collection of unit vectors in ℝn such that the distance between two distinct vectors assumes one of only two values. We use the semidefinite programming method to compute improved estimates of the maximum size of spherical two-distance sets. Exact answers are found for dimensions n = 23 and 40 ≤ n ≤ 93 (n ≠ 46, 78), where previous results gave divergent bounds.

AB - A spherical two-distance set is a finite collection of unit vectors in ℝn such that the distance between two distinct vectors assumes one of only two values. We use the semidefinite programming method to compute improved estimates of the maximum size of spherical two-distance sets. Exact answers are found for dimensions n = 23 and 40 ≤ n ≤ 93 (n ≠ 46, 78), where previous results gave divergent bounds.

KW - Positive definite matrices

KW - Semidefinite programming

KW - Two-distance sets

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New bounds for spherical two-distance sets

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Keywords

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