{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T10:25:46Z","timestamp":1760523946753,"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>\r\n\r\n\r\nA $q$-covering design $\\mathbb{C}_q (n, k, r)$, $k \\ge r$, is a collection $\\mathcal{X}$ of $(k-1)$-spaces of $PG(n-1, q)$ such that every $(r-1)$-space of $PG(n-1,q)$ is contained in at least one element of $\\mathcal{X}$ . Let $\\mathcal{C}_q(n, k, r)$ denote the minimum number of $(k-1)$-spaces in a $q$-covering design $\\mathbb{C}_q (n, k, r)$. In this paper improved upper bounds on $\\mathcal{C}_q(2n, 3, 2)$, $n \\ge 4$, $\\mathcal{C}_q(3n + 8, 4, 2)$, $n \\ge 0$, and $\\mathcal{C}_q(2n,4,3)$, $n \\ge 4$, are presented. The results are achieved by constructing the related $q$-covering designs.\r\n\r\n\r\n<\/jats:p>","DOI":"10.37236\/8718","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T10:04:55Z","timestamp":1581069895000},"source":"Crossref","is-referenced-by-count":1,"title":["On $q$-Covering Designs"],"prefix":"10.37236","volume":"27","author":[{"given":"Francesco","family":"Pavese","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,2,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p35\/8025","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p35\/8025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T10:04:55Z","timestamp":1581069895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8718","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,2,7]]},"article-number":"P1.35"}}