{"paper":{"title":"Double blocking sets of size $3q-1$ in $\\mathrm{PG}(2,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bence Csajb\\'ok, Tam\\'as H\\'eger","submitted_at":"2018-05-03T12:51:11Z","abstract_excerpt":"The main purpose of this paper is to find double blocking sets in $\\mathrm{PG}(2,q)$ of size less than $3q$, in particular when $q$ is prime. To this end, we study double blocking sets in $\\mathrm{PG}(2,q)$ of size $3q-1$ admitting at least two $(q-1)$-secants. We derive some structural properties of these and show that they cannot have three $(q-1)$-secants. This yields that one cannot remove six points from a triangle, a double blocking set of size $3q$, and add five new points so that the resulting set is also a double blocking set. Furthermore, we give constructions of minimal double block"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01267","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}