Semidefinite Programming Bounds For Spherical Three-distance Sets

Abstract

A spherical three-distance set is a finite collection $X$ of unit vectors in ${\mathbb{R}}^n$ such that for each pair of distinct vectors has three inner product values. We use the semidefinite programming method to improve the upper bounds of spherical three-distance sets for 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 maximum size of spherical three-distance sets is $2300$ in ${\mathbb{R}}^{23}$.

10 pages

References in corpus (1)

• New upper bounds for kissing numbers from semidefinite programming