{"paper":{"title":"Maximal determinants and saturated D-optimal designs of orders 19 and 37","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.CO","authors_text":"Judy-anne Osborn, Paul Zimmermann, Richard P. Brent, William Orrick","submitted_at":"2011-12-18T14:09:00Z","abstract_excerpt":"A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal. For order 19 we find all inequivalent saturated D-optimal designs with maximal determinant, 2^30 x 7^2 x 17, and confirm that the three known designs comprise a complete set. For order 37 we prove that the maximal determinant is 2^39 x 3^36, and find a sample of inequivalent saturated D-optimal designs. Our method is an extension of that used by Orrick to r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4160","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"}