{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833537,"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>An $(n,r,s)$-system is an $r$-uniform hypergraph on $n$ vertices such that every pair of edges has an intersection of size less than $s$. Using probabilistic arguments, R\u00f6dl and \u0160i\u0148ajov\u00e1 showed that for all fixed integers $r&gt; s \\ge 2$, there exists an $(n,r,s)$-system with independence number $O\\left(n^{1-\\delta+o(1)}\\right)$ for some optimal constant $\\delta &gt;0$ only related to $r$ and $s$. We show that for certain pairs $(r,s)$ with $s\\le r\/2$ there exists an explicit construction of an $(n,r,s)$-system with independence number $O\\left(n^{1-\\epsilon}\\right)$, where $\\epsilon &gt; 0$ is an absolute constant only related to $r$ and $s$. Previously this was known only for $s&gt;r\/2$ by results of Chattopadhyay and Goodman.<\/jats:p>","DOI":"10.37236\/10513","type":"journal-article","created":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:51:00Z","timestamp":1649033460000},"source":"Crossref","is-referenced-by-count":1,"title":["On Explicit Constructions of Designs"],"prefix":"10.37236","volume":"29","author":[{"given":"Xizhi","family":"Liu","sequence":"first","affiliation":[]},{"given":"Dhruv","family":"Mubayi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,3,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p53\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:51:00Z","timestamp":1649033460000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i1p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1,27]]}},"URL":"https:\/\/doi.org\/10.37236\/10513","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,3,25]]},"article-number":"P1.53"}}