{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:04Z","timestamp":1753893844580,"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 $k_3(n)$ denote the minimal cardinality of a ternary code of length $n$ and covering radius one. In this paper we show $k_3(7)\\ge 156$ and $k_3(8)\\ge 402$ improving on the best previously known bounds $k_3(7)\\ge 153$ and $k_3(8)\\ge 398$. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie in $k$-dimensional subspaces of F${}_3^n$.<\/jats:p>","DOI":"10.37236\/945","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:51:27Z","timestamp":1578718287000},"source":"Crossref","is-referenced-by-count":0,"title":["Lower Bounds for the Football Pool Problem for 7 and 8 Matches"],"prefix":"10.37236","volume":"14","author":[{"given":"Wolfgang","family":"Haas","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,3,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:04:10Z","timestamp":1579320250000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,3,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/945","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,3,28]]},"article-number":"R27"}}