{"paper":{"title":"Tables, bounds and graphics of sizes of complete arcs in the plane $\\mathrm{PG}(2,q)$ for all $q\\le321007$ and sporadic $q$ in $[323761\\ldots430007]$ obtained by an algorithm with fixed order of points (FOP)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander A. Davydov, Alexey A. Kreshchuk, Daniele Bartoli, Fernanda Pambianco, Giorgio Faina, Stefano Marcugini","submitted_at":"2014-04-02T06:26:19Z","abstract_excerpt":"In the previous works of the authors, a step-by-step algorithm FOP which uses any fixed order of points in the projective plane $\\mathrm{PG}(2,q)$ is proposed to construct small complete arcs. In each step, the algorithm adds to a current arc the first point in the fixed order not lying on the bisecants of the arc. The algorithm is based on the intuitive postulate that $\\mathrm{PG}(2,q)$ contains a sufficient number of relatively small complete arcs. Also, in the previous papers, it is shown that the type of order on the points of $\\mathrm{PG}(2,q)$ is not relevant. A complete lexiarc in $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0469","kind":"arxiv","version":3},"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"}