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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}&\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.2155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-08T00:04:08Z","cross_cats_sorted":[],"title_canon_sha256":"47b23bfd8ab51b2fa073fc3a0e392e01461272d796cf256405f654d1b6c4196d","abstract_canon_sha256":"f85eac60534f42611ec8b00d21192c3ed84d18a94c75b3fee4b90cec1ac234ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:47.606113Z","signature_b64":"ZHUY1MIRXyj2bqnynUTwEkz4MjQN7VQe4uMOvPwoZ+AIYyfNKoreZTcgk6DtzxB9IkaBorm8T5fnm8TrMCreCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56fe4e54d1d0924cc7ca642c81a25a0d20ab08b530463032da78e1105da72bd7","last_reissued_at":"2026-05-18T01:37:47.605692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:47.605692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1312.2155","created_at":"2026-05-18T01:37:47.605754+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.2155v3","created_at":"2026-05-18T01:37:47.605754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2155","created_at":"2026-05-18T01:37:47.605754+00:00"},{"alias_kind":"pith_short_12","alias_value":"K37E4VGR2CJE","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"K37E4VGR2CJEZR6K","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"K37E4VGR","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU","json":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU.json","graph_json":"https://pith.science/api/pith-number/K37E4VGR2CJEZR6KMQWIDIS2BU/graph.json","events_json":"https://pith.science/api/pith-number/K37E4VGR2CJEZR6KMQWIDIS2BU/events.json","paper":"https://pith.science/paper/K37E4VGR"},"agent_actions":{"view_html":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU","download_json":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU.json","view_paper":"https://pith.science/paper/K37E4VGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.2155&json=true","fetch_graph":"https://pith.science/api/pith-number/K37E4VGR2CJEZR6KMQWIDIS2BU/graph.json","fetch_events":"https://pith.science/api/pith-number/K37E4VGR2CJEZR6KMQWIDIS2BU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU/action/storage_attestation","attest_author":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU/action/author_attestation","sign_citation":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU/action/citation_signature","submit_replication":"https://pith.science/pith/K37E4VGR2CJEZR6KMQWIDIS2BU/action/replication_record"}},"created_at":"2026-05-18T01:37:47.605754+00:00","updated_at":"2026-05-18T01:37:47.605754+00:00"}