### Abstract

A set of lines through the origin in Euclidean space is called equiangular when any pair of lines from the set intersects with each other at a common angle. We study the maximum size of equiangular lines in Euclidean space and use a graph theoretic approach to prove that all the currently known constructions for maximum equiangular lines in R^{d} cannot be added by any more lines to form a larger equiangular set of lines when d=14,16,17,18,19, and 20. We give new constructions of large equiangular lines which are 248 equiangular lines in R^{42}, 200 equiangular lines in R^{41}, 168 equiangular lines in R^{40}, 152 equiangular lines in R^{39} with angle 1/7, and 56 equiangular lines in R^{18} with angle 1/5.

Original language | English |
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Pages (from-to) | 272-281 |

Number of pages | 10 |

Journal | Linear Algebra and Its Applications |

Volume | 588 |

DOIs | |

Publication status | Published - 2020 Mar 1 |

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### Keywords

- Clique number
- Equiangular lines

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

### Cite this

*Linear Algebra and Its Applications*,

*588*, 272-281. https://doi.org/10.1016/j.laa.2019.12.002