Equiangular lines in low dimensional Euclidean spaces

We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19 and 20 dimensions to 74 and 94, respectively.

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Main Authors:	Greaves, Gary Royden Watson, Syatriadi, Jeven, Yatsyna, Pavlo
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2021
Subjects:	Science::Mathematics::Discrete mathematics::Combinatorics Science::Mathematics::Discrete mathematics::Theory of computation Spherical Codes Equiangular
Online Access:	https://hdl.handle.net/10356/152761
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Institution:	Nanyang Technological University
Language:	English

id	sg-ntu-dr.10356-152761
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spelling	sg-ntu-dr.10356-1527612021-12-11T11:06:32Z Equiangular lines in low dimensional Euclidean spaces Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo School of Physical and Mathematical Sciences Science::Mathematics::Discrete mathematics::Combinatorics Science::Mathematics::Discrete mathematics::Theory of computation Spherical Codes Equiangular We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19 and 20 dimensions to 74 and 94, respectively. Ministry of Education (MOE) GRWG was supported by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG29/18 and RG21/20. PY was supported by project PRIMUS/20/SCI/002 from Charles University 2021-12-11T11:06:32Z 2021-12-11T11:06:32Z 2021 Journal Article Greaves, G. R. W., Syatriadi, J. & Yatsyna, P. (2021). Equiangular lines in low dimensional Euclidean spaces. Combinatorica. https://dx.doi.org/10.1007/s00493-020-4523-0 0209-9683 https://hdl.handle.net/10356/152761 10.1007/s00493-020-4523-0 2-s2.0-85113999320 en RG29/18 RG21/20 Combinatorica © 2021 János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg. All rights reserved.
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Science::Mathematics::Discrete mathematics::Combinatorics Science::Mathematics::Discrete mathematics::Theory of computation Spherical Codes Equiangular
spellingShingle	Science::Mathematics::Discrete mathematics::Combinatorics Science::Mathematics::Discrete mathematics::Theory of computation Spherical Codes Equiangular Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo Equiangular lines in low dimensional Euclidean spaces
description	We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19 and 20 dimensions to 74 and 94, respectively.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo
format	Article
author	Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo
author_sort	Greaves, Gary Royden Watson
title	Equiangular lines in low dimensional Euclidean spaces
title_short	Equiangular lines in low dimensional Euclidean spaces
title_full	Equiangular lines in low dimensional Euclidean spaces
title_fullStr	Equiangular lines in low dimensional Euclidean spaces
title_full_unstemmed	Equiangular lines in low dimensional Euclidean spaces
title_sort	equiangular lines in low dimensional euclidean spaces
publishDate	2021
url	https://hdl.handle.net/10356/152761
_version_	1718928719305768960

Equiangular lines in low dimensional Euclidean spaces

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