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A 2-distance set with 277 points in the Euclidean space of dimension 23

Hong-Jun Ge, Jack Koolen, Akihiro Munemasa

Abstract

We construct a $2$-distance set with $277$ points in the $23$-dimensional Euclidean space having distances $2$ and $\sqrt{6}$.

A 2-distance set with 277 points in the Euclidean space of dimension 23

Abstract

We construct a -distance set with points in the -dimensional Euclidean space having distances and .

Paper Structure

This paper contains 4 sections, 3 theorems, 15 equations.

Table of Contents

  1. Introduction
  2. The Construction
  3. Maximality
  4. Magma code

Key Result

Theorem 1

The set $Z:=\{\mathbf{u}\}\cup X\cup Y$ is a $2$-distance set of size $277$ with squared distances $\{4,6\}$, contained in the affine hyperplane $\{\mathbf{v}\in\mathbb{R}^{24}\mid \langle \mathbf{v},\mathbf{r}\rangle=1\}\cong\mathbb{R}^{23}$.

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Lemma 2
  • proof
  • Proposition 3
  • proof