English

$k$-point semidefinite programming bounds for equiangular lines

Optimization and Control 2022-06-30 v2 Metric Geometry

Abstract

We give a hierarchy of kk-point bounds extending the Delsarte-Goethals-Seidel linear programming 22-point bound and the Bachoc-Vallentin semidefinite programming 33-point bound for spherical codes. An optimized implementation of this hierarchy allows us to compute~44, 55, and 66-point bounds for the maximum number of equiangular lines in Euclidean space with a fixed common angle.

Keywords

Cite

@article{arxiv.1812.06045,
  title  = {$k$-point semidefinite programming bounds for equiangular lines},
  author = {David de Laat and Fabrício Caluza Machado and Fernando Mário de Oliveira Filho and Frank Vallentin},
  journal= {arXiv preprint arXiv:1812.06045},
  year   = {2022}
}

Comments

26 pages, 4 figures. New introduction and references updated

R2 v1 2026-06-23T06:42:51.770Z