{"paper":{"title":"On the Optimality of the Kautz-Singleton Construction in Probabilistic Group Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ayfer Ozgur, Huseyin A. Inan, Mary Wootters, Peter Kairouz","submitted_at":"2018-08-04T09:30:44Z","abstract_excerpt":"We consider the probabilistic group testing problem where $d$ random defective items in a large population of $N$ items are identified with high probability by applying binary tests. It is known that $\\Theta(d \\log N)$ tests are necessary and sufficient to recover the defective set with vanishing probability of error when $d = O(N^{\\alpha})$ for some $\\alpha \\in (0, 1)$. However, to the best of our knowledge, there is no explicit (deterministic) construction achieving $\\Theta(d \\log N)$ tests in general. In this work, we show that a famous construction introduced by Kautz and Singleton for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01457","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"}