{"paper":{"title":"Upper bounds on the smallest size of a complete arc in the plane PG(2,q)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Alexander A. Davydov, Daniele Bartoli, Fernanda Pambianco, Giorgio Faina, Stefano Marcugini","submitted_at":"2011-11-15T01:34:18Z","abstract_excerpt":"New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for q <= 9109. From these new bounds it follows that for q <= 2621 and q = 2659,2663,2683,2693,2753,2801, the relation t_{2}(2,q) < 4.5\\sqrt{q} holds. Also, for q <= 5399 and q = 5413,5417,5419,5441,5443,5471,5483,5501,5521, we have t_{2}(2,q) < 4.8\\sqrt{q}. Finally, for q <= 9067 it holds that t_{2}(2,q) < 5\\sqrt{q}. The new upper bounds are obtained by finding new small complete arcs with the help of a computer search using randomized greedy algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3403","kind":"arxiv","version":1},"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"}