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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."},"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":"1111.3403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-15T01:34:18Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"af4bce711c8329f5ea231a4a3700559dd1c98e99d631d9b198e240e801819c84","abstract_canon_sha256":"a86a4e60574f55f3360fbdea6f991fa6d28bc53c9ca71eec8a8a9eb5c926f236"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:14.150311Z","signature_b64":"lCj41kiQ8/UYoTcoTq591oEZWQOmyt64ByEbqnYss5NtIpkAr2GVOXIqMep0p7tBMYumiG7cZ/LUTivpA6/8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d29ce74fd80836908ea7e549d2a825ca90a62bd62c369669add8b881a144c884","last_reissued_at":"2026-05-18T04:08:14.149890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:14.149890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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}. 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