{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:35Z","timestamp":1753893815626,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, by using properties of Baer subplanes, we describe the construction of a minimal blocking set in the Hall plane of order $q^2$ of size $q^2+2q+2$ admitting $1-$, $2-$, $3-$, $4-$, $(q+1)-$ and $(q+2)-$secants. As a corollary, we obtain the existence of a minimal blocking set of a non-Desarguesian affine plane of order $q^2$ of size at most $4q^2\/3+5q\/3$, which is considerably smaller than $2q^2-1$, the Jamison bound for the size of a minimal blocking set in an affine Desarguesian plane of order $q^2$.We also consider particular Andr\u00e9 planes of order $q$, where $q$ is a\u00a0power of the prime $p$, and give a construction of a small minimal blocking set which admits a secant line not meeting the blocking set in $1$ mod $p$ points. Furthermore, we elaborate on the connection of this problem with the study of value sets of certain polynomials and with the construction\u00a0of small double blocking sets in Desarguesian projective planes; in both topics we provide some new results.<\/jats:p>","DOI":"10.37236\/5717","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:29:07Z","timestamp":1578691747000},"source":"Crossref","is-referenced-by-count":3,"title":["Blocking and Double Blocking Sets in Finite Planes"],"prefix":"10.37236","volume":"23","author":[{"given":"Jan","family":"De Beule","sequence":"first","affiliation":[]},{"given":"Tam\u00e1s","family":"H\u00e9ger","sequence":"additional","affiliation":[]},{"given":"Tam\u00e1s","family":"Sz\u0151nyi","sequence":"additional","affiliation":[]},{"given":"Geertrui","family":"Van de Voorde","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,4,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:30:33Z","timestamp":1579239033000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5717","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,4,1]]},"article-number":"P2.5"}}