{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GTVASFFU4U4BK2R5MBUCOR6ENR","short_pith_number":"pith:GTVASFFU","schema_version":"1.0","canonical_sha256":"34ea0914b4e538156a3d60682747c46c5ceae14b25619aa088ce0cbbacd19496","source":{"kind":"arxiv","id":"1503.08876","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic size of covering arrays: an application of entropy compression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brett Stevens, Nevena Franceti\\'c","submitted_at":"2015-03-31T00:04:00Z","abstract_excerpt":"A covering array $CA(N; t,k,v)$ is an $N \\times k$ array $A$ whose each cell takes a value for a $v$-set $V$ called an alphabet. Moreover, the set $V^t$ is contained in the set of rows of every $N \\times t$ subarray of $A$. The parameter $N$ is called the size of an array and $CAN(t,k,v)$ denotes the smallest $N$ for which a $CA(N; t,k,v)$ exists. It is well known that $CAN(t,k,v) = {\\rm \\Theta}(\\log_2 k)$~\\cite{godbole_bounds_1996}. In this paper we derive two upper bounds on $d(t,v)=\\limsup_{k \\rightarrow \\infty} \\frac{CAN(t,k,v)}{\\log_2 k}$ using the algorithmic approach to the Lov\\'{a}sz l"},"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":"1503.08876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-31T00:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"68ceb874be473ad9979bfabc4c40ad240fef1d0122ddf895fc3d9291ca1ccbaa","abstract_canon_sha256":"9ba54b9745a49bef86c9392448a73edf12b6f9b2fbd0184f5f7b968dd0d2e0fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:51.964518Z","signature_b64":"brw4cBqHBo3Fqe/QQdEN0saCmhX/BK7CtXtXWgi3aTIUEt71LFCVwhNGOGQPotqvL0mzGdUZF98EQAIpzBpBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34ea0914b4e538156a3d60682747c46c5ceae14b25619aa088ce0cbbacd19496","last_reissued_at":"2026-05-18T02:19:51.963783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:51.963783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic size of covering arrays: an application of entropy compression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brett Stevens, Nevena Franceti\\'c","submitted_at":"2015-03-31T00:04:00Z","abstract_excerpt":"A covering array $CA(N; t,k,v)$ is an $N \\times k$ array $A$ whose each cell takes a value for a $v$-set $V$ called an alphabet. Moreover, the set $V^t$ is contained in the set of rows of every $N \\times t$ subarray of $A$. The parameter $N$ is called the size of an array and $CAN(t,k,v)$ denotes the smallest $N$ for which a $CA(N; t,k,v)$ exists. It is well known that $CAN(t,k,v) = {\\rm \\Theta}(\\log_2 k)$~\\cite{godbole_bounds_1996}. In this paper we derive two upper bounds on $d(t,v)=\\limsup_{k \\rightarrow \\infty} \\frac{CAN(t,k,v)}{\\log_2 k}$ using the algorithmic approach to the Lov\\'{a}sz l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08876","kind":"arxiv","version":1},"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":"1503.08876","created_at":"2026-05-18T02:19:51.963909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08876v1","created_at":"2026-05-18T02:19:51.963909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08876","created_at":"2026-05-18T02:19:51.963909+00:00"},{"alias_kind":"pith_short_12","alias_value":"GTVASFFU4U4B","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GTVASFFU4U4BK2R5","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GTVASFFU","created_at":"2026-05-18T12:29:22.688609+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/GTVASFFU4U4BK2R5MBUCOR6ENR","json":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR.json","graph_json":"https://pith.science/api/pith-number/GTVASFFU4U4BK2R5MBUCOR6ENR/graph.json","events_json":"https://pith.science/api/pith-number/GTVASFFU4U4BK2R5MBUCOR6ENR/events.json","paper":"https://pith.science/paper/GTVASFFU"},"agent_actions":{"view_html":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR","download_json":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR.json","view_paper":"https://pith.science/paper/GTVASFFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08876&json=true","fetch_graph":"https://pith.science/api/pith-number/GTVASFFU4U4BK2R5MBUCOR6ENR/graph.json","fetch_events":"https://pith.science/api/pith-number/GTVASFFU4U4BK2R5MBUCOR6ENR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR/action/storage_attestation","attest_author":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR/action/author_attestation","sign_citation":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR/action/citation_signature","submit_replication":"https://pith.science/pith/GTVASFFU4U4BK2R5MBUCOR6ENR/action/replication_record"}},"created_at":"2026-05-18T02:19:51.963909+00:00","updated_at":"2026-05-18T02:19:51.963909+00:00"}