A spherical three-distance set is a finite collection $X$ of unit vectors in $\mathbb{R}^{n}$ such that the set of the distances between any two distinct vectors has cardinality three. We use the semidefinite programming method to improve the upper bounds for the cardinalities of spherical three-distance sets in the Euclidean spaces of several dimensions. We obtain better bounds in $\mathbb{R}^7$, $\mathbb{R}^{20}$, $\mathbb{R}^{21}$, $\mathbb{R}^{23}$, $\mathbb{R}^{24}$ and $\mathbb{R}^{25}$. In particular, we prove that the maximum cardinality of a spherical three-distance set in $\mathbb R^{23}$ is $2300$.
@article{10_37236_11979,
author = {Wei-Hsuan Yu and Feng-Yuan Liu},
title = {Semidefinite programming bounds for spherical three-distance sets},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/11979},
zbl = {7940954},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11979/}
}
TY - JOUR
AU - Wei-Hsuan Yu
AU - Feng-Yuan Liu
TI - Semidefinite programming bounds for spherical three-distance sets
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11979/
DO - 10.37236/11979
ID - 10_37236_11979
ER -
%0 Journal Article
%A Wei-Hsuan Yu
%A Feng-Yuan Liu
%T Semidefinite programming bounds for spherical three-distance sets
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11979/
%R 10.37236/11979
%F 10_37236_11979
Wei-Hsuan Yu; Feng-Yuan Liu. Semidefinite programming bounds for spherical three-distance sets. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/11979
