{"paper":{"title":"$t$-Covering Arrays Generated by a Tiling Probability Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"math.CO","authors_text":"Anant P. Godbole, Michael S. Donders","submitted_at":"2010-11-01T15:40:49Z","abstract_excerpt":"A $t-\\a$ covering array is an $m\\times n$ matrix, with entries from an alphabet of size $\\alpha$, such that for any choice of $t$ rows, and any ordered string of $t$ letters of the alphabet, there exists a column such that the \"values\" of the rows in that column match those of the string of letters. We use the Lov\\'asz Local Lemma in conjunction with a new tiling-based probability model to improve the upper bound on the smallest number of columns $N=N(m,t,\\alpha)$ of a $t-\\a$ covering array."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0351","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"}