{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822999,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 Gr\u00f6bner 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.<\/jats:p>","DOI":"10.37236\/8565","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T09:18:35Z","timestamp":1579857515000},"source":"Crossref","is-referenced-by-count":6,"title":["Constructions of Maximum Few-Distance Sets in Euclidean Spaces"],"prefix":"10.37236","volume":"27","author":[{"given":"Ferenc","family":"Sz\u00f6ll\u0151si","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patric R.J.","family":"\u00d6sterg\u00e5rd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,1,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p23\/8009","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p23\/8009","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T09:18:35Z","timestamp":1579857515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8565","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,24]]},"article-number":"P1.23"}}