{"paper":{"title":"New lower bounds for $t$-coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Horsley, Rakhi Singh","submitted_at":"2017-06-21T11:08:26Z","abstract_excerpt":"Fisher proved in 1940 that any $2$-$(v,k,\\lambda)$ design with $v>k$ has at least $v$ blocks. In 1975 Ray-Chaudhuri and Wilson generalised this result by showing that every $t$-$(v,k,\\lambda)$ design with $v \\geq k+\\lfloor t/2 \\rfloor$ has at least $\\binom{v}{\\lfloor t/2 \\rfloor}$ blocks. By combining methods used by Bose and Wilson in proofs of these results, we obtain new lower bounds on the size of $t$-$(v,k,\\lambda)$ coverings. Our results generalise lower bounds on the size of $2$-$(v,k,\\lambda)$ coverings recently obtained by the first author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06825","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"}