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Davydov, Daniele Bartoli, Fernanda Pambianco, Giorgio Faina, Stefano Marcugini","submitted_at":"2010-11-15T11:36:43Z","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 853 <= q <= 4561 and q\\in T1\\cup T2 where T1={173,181,193,229,243,257,271,277,293,343,373,409,443,449,457, 461,463,467,479,487,491,499,529,563,569,571,577,587,593,599,601,607,613,617,619,631, 641,661,673,677,683,691, 709}, T2={4597,4703,4723,4733,4789,4799,4813,4831,5003,5347,5641,5843,6011,8192}. From these new bounds it follows that for q <= 2593 and q=2693,2753, the relation t_{2}(2,q) < 4.5\\sqrt{q} holds. Also, for q <= 4561 we have t_{2}(2,q) < 4.75\\sqrt{q}. It is showed tha"},"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":"1011.3347","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-15T11:36:43Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"d29d2f5b6f483f875c817591ff3a95aa12d1d373f45ead7a29dada7e79209168","abstract_canon_sha256":"011c313c8549b9973fe0db3865a5c536072e6e2f58d736fc3894677a2a63ac60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:29.879575Z","signature_b64":"TRvRsG6GgmQa75Ty0gA+h11EI2ZXX4i+V5cZT15qL8iQdjB/n/jQJJRfzr6upNNujgtyxTu5VmcbjMLuoNEqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5411a91ab75afa173c551ded1d219d258027006328539c8adf7c5c2fa34faa7f","last_reissued_at":"2026-05-18T04:21:29.879231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:29.879231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On sizes of complete arcs in 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":"2010-11-15T11:36:43Z","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 853 <= q <= 4561 and q\\in T1\\cup T2 where T1={173,181,193,229,243,257,271,277,293,343,373,409,443,449,457, 461,463,467,479,487,491,499,529,563,569,571,577,587,593,599,601,607,613,617,619,631, 641,661,673,677,683,691, 709}, T2={4597,4703,4723,4733,4789,4799,4813,4831,5003,5347,5641,5843,6011,8192}. From these new bounds it follows that for q <= 2593 and q=2693,2753, the relation t_{2}(2,q) < 4.5\\sqrt{q} holds. Also, for q <= 4561 we have t_{2}(2,q) < 4.75\\sqrt{q}. 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