{"paper":{"title":"Partial Covering Arrays: Algorithms and Asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Annalisa De Bonis, Charles J. Colbourn, Kaushik Sarkar, Ugo Vaccaro","submitted_at":"2016-05-07T02:09:26Z","abstract_excerpt":"A covering array $\\mathsf{CA}(N;t,k,v)$ is an $N\\times k$ array with entries in $\\{1, 2, \\ldots , v\\}$, for which every $N\\times t$ subarray contains each $t$-tuple of $\\{1, 2, \\ldots , v\\}^t$ among its rows. Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems. A central question is to determine or bound $\\mathsf{CAN}(t,k,v)$, the minimum number $N$ of rows of a $\\mathsf{CA}(N;t,k,v)$. The well known bound $\\mathsf{CAN}(t,k,v)=O((t-1)v^t\\log k)$ is not too far from being asymptotically optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02131","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"}