Constructions of maximum few-distance sets in euclidean spaces

Patric R.J. Östergård*, Ferenc Szollosi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
83 Downloads (Pure)


A finite set of vectors X in the d-dimensional Euclidean space Rd is called an s-distance set if the set of mutual distances between distinct elements of 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 R4, the largest 4-distance sets in R3, and the largest 6-distance sets in R2. We also construct new examples of large s-distance sets in Rd for d ≤ 8 and s ≤ 6, and independently verify several earlier results from the literature.

Original languageEnglish
Article numberP1.23
Number of pages18
JournalElectronic Journal of Combinatorics
Issue number1
Publication statusPublished - 24 Jan 2020
MoE publication typeA1 Journal article-refereed


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