{"paper":{"title":"On the Structure of Small Strength-$2$ Covering Arrays","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brett Stevens, Janne I. Kokkala, Karen Meagher, Kari J. Nurmela, Patric R. J. \\\"Osterg{\\aa}rd, Reza Naserasr","submitted_at":"2019-01-11T14:30:24Z","abstract_excerpt":"A covering array $\\rm{CA}(N;t,k,v)$ of strength $t$ is an $N \\times k$ array of symbols from an alphabet of size $v$ such that in every $N \\times t$ subarray, every $t$-tuple occurs in at least one row. A covering array is \\emph{optimal} if it has the smallest possible $N$ for given $t$, $k$, and $v$, and \\emph{uniform} if every symbol occurs $\\lfloor N/v \\rfloor$ or $\\lceil N/v \\rceil$ times in every column. Prior to this paper the only known optimal covering arrays for $t=2$ were orthogonal arrays, covering arrays with $v=2$ constructed from Sperner's Theorem and the Erd\\H{o}s-Ko-Rado Theore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03594","kind":"arxiv","version":2},"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"}