# $k$-point semidefinite programming bounds for equiangular lines

## TL;DR

This paper introduces a hierarchy of $k$-point semidefinite programming bounds that extend existing bounds for spherical codes, enabling the computation of bounds for the maximum number of equiangular lines with fixed angles.

## Contribution

It develops a new hierarchy of $k$-point bounds that generalize previous bounds and provides optimized methods to compute these bounds for higher points.

## Key findings

- Successfully computed 4, 5, and 6-point bounds for equiangular lines.
- Extended the existing bounds from 2-point and 3-point to higher points.
- Enhanced the accuracy of bounds for equiangular lines in Euclidean space.

## Abstract

We give a hierarchy of $k$-point bounds extending the Delsarte-Goethals-Seidel linear programming $2$-point bound and the Bachoc-Vallentin semidefinite programming $3$-point bound for spherical codes. An optimized implementation of this hierarchy allows us to compute~$4$, $5$, and $6$-point bounds for the maximum number of equiangular lines in Euclidean space with a fixed common angle.