{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:02Z","timestamp":1753893842630,"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>Let $\\mathcal{S}$ be a regular near octagon with $s+1=3$ points per line, let $t+1$ denote the constant number of lines through a given point of $\\mathcal{S}$ and for every two points $x$ and $y$ at distance $i \\in \\{ 2,3 \\}$ from each other, let $t_i+1$ denote the constant number of lines through $y$ containing a (necessarily unique) point at distance $i-1$ from $x$. It is known, using algebraic combinatorial techniques, that $(t_2,t_3,t)$ must be equal to either $(0,0,1)$, $(0,0,4)$, $(0,3,4)$, $(0,8,24)$, $(1,2,3)$, $(2,6,14)$ or $(4,20,84)$. For all but one of these cases, there is a unique example of a regular near octagon known. In this paper, we deal with the existence question for the remaining case. We prove that no regular near octagons with parameters $(s,t,t_2,t_3)=(2,24,0,8)$ can exist.<\/jats:p>","DOI":"10.37236\/421","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:59:41Z","timestamp":1578697181000},"source":"Crossref","is-referenced-by-count":2,"title":["The Nonexistence of Regular Near Octagons with Parameters $(s,t,t_2,t_3)=(2,24,0,8)$"],"prefix":"10.37236","volume":"17","author":[{"given":"Bart","family":"De Bruyn","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,11,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r149\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r149\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:22:12Z","timestamp":1579285332000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r149"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/421","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,11,5]]},"article-number":"R149"}}