A finite set of vectors $\mathcal{X}$ in the $d$-dimensional Euclidean space $\mathbb{R}^d$ is called an $s$-distance set if the set of mutual distances between distinct elements of $\mathcal{X}$ has cardinality exactly $s$. In this paper we present a combined approach of isomorph-free exhaustive generation of graphs and Gröbner basis computation to classify the largest $3$-distance sets in $\mathbb{R}^4$, the largest $4$-distance sets in $\mathbb{R}^3$, and the largest $6$-distance sets in $\mathbb{R}^2$. We also construct new examples of large $s$-distance sets in $\mathbb{R}^d$ for $d\leq 8$ and $s\leq 6$, and independently verify several earlier results from the literature.
@article{10_37236_8565,
author = {Ferenc Sz\"oll\H{o}si and Patric R.J. \"Osterg\r{a}rd},
title = {Constructions of maximum few-distance sets in {Euclidean} spaces},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/8565},
zbl = {1454.51007},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8565/}
}
TY - JOUR
AU - Ferenc Szöllősi
AU - Patric R.J. Östergård
TI - Constructions of maximum few-distance sets in Euclidean spaces
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8565/
DO - 10.37236/8565
ID - 10_37236_8565
ER -
%0 Journal Article
%A Ferenc Szöllősi
%A Patric R.J. Östergård
%T Constructions of maximum few-distance sets in Euclidean spaces
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8565/
%R 10.37236/8565
%F 10_37236_8565
Ferenc Szöllősi; Patric R.J. Östergård. Constructions of maximum few-distance sets in Euclidean spaces. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8565
