{"paper":{"title":"Universal Sets and Cover-Free Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Debjyoti Saharoy, Shailesh Vaya","submitted_at":"2016-06-04T13:32:39Z","abstract_excerpt":"We propose a polynomial time construction of an $(n,d)$-universal set over alphabet $\\Sigma=\\{0,1\\}$, of size $d\\cdot 2^{d+o(d)}\\cdot\\log n$. This is an improvement over the size, $d^{5}2^{2.66d}\\log n$, of an $(n,d)$-universal set constructed by Bshouty, \\cite{BshoutyTesters}, over alphabet $\\Sigma=\\{0,1\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01376","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"}