{"paper":{"title":"Tables, bounds and graphics of the smallest known sizes of complete arcs in the plane $\\mathrm{PG}(2,q)$ for all $q\\le160001$ and sporadic $q$ in the interval $[160801\\ldots 430007]$","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":"2013-12-08T00:04:08Z","abstract_excerpt":"In the projective planes $\\mathrm{PG}(2,q)$, we collect the smallest known sizes of complete arcs for the regions \\begin{align*} &\\mbox{all } q\\le160001,~~ q \\mbox{ prime power};\\\\ &Q_{4}=\\{34 \\mbox{ sporadic }q'\\mbox{s in the interval }[160801\\ldots430007], \\mbox{ see Table 3}\\}. \\end{align*}\n  For $q\\le160001$, the collection of arc sizes is complete in the sense that arcs for all prime powers are considered. This proves new upper bounds on the smallest size $t_{2}(2,q)$ of a complete arc in $\\mathrm{PG}(2,q)$, in particular \\begin{align*} t_{2}(2,q)&<0.998\\sqrt{3q\\ln q}<1.729\\sqrt{q\\ln q}&\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2155","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"}