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

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

23 引文斯高帕斯（Scopus）

摘要

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.

原文	???core.languages.en_GB???
頁（從 - 到）	187-194
頁數	8
期刊	Experimental Mathematics
卷	22
發行號	2
DOIs	https://doi.org/10.1080/10586458.2013.767725
出版狀態	已出版 - 3 4月 2013

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10.1080/10586458.2013.767725

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

author = "Alexander Barg and Yu, \{Wei Hsuan\}",

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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