{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T14:53:12Z","timestamp":1776955992158,"version":"3.51.4"},"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>The group PGL$(2,q)$, $q=p^n$, $p$ an odd prime, is $3$-transitive on the projective line and therefore it can be used to construct $3$-designs. In this paper, we determine the sizes of orbits from the action of PGL$(2,q)$ on the $k$-subsets of the projective line when $k$ is not congruent to $0$ and 1 modulo $p$. Consequently, we find all values of $\\lambda$ for which there exist $3$-$(q+1,k,\\lambda)$ designs admitting PGL$(2,q)$ as automorphism group. In the case $p\\equiv 3$ mod 4, the results and some previously known facts are used to classify 3-designs from PSL$(2,p)$ up to isomorphism.<\/jats:p>","DOI":"10.37236\/1076","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:00:01Z","timestamp":1578718801000},"source":"Crossref","is-referenced-by-count":49,"title":["$3$-Designs from PGL$(2,q)$"],"prefix":"10.37236","volume":"13","author":[{"given":"P. J.","family":"Cameron","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. R.","family":"Omidi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Tayfeh-Rezaie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2006,5,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:10:52Z","timestamp":1579320652000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1076","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,5,19]]},"article-number":"R50"}}