{"paper":{"title":"A note on the minimum size of an orthogonal array","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Jay H. Beder, Margaret Ann McComack","submitted_at":"2015-08-24T21:47:16Z","abstract_excerpt":"It is an elementary fact that the size of an orthogonal array of strength t on k factors must be a multiple of a certain number, say L_t, that depends on the orders of the factors. Thus L_t is a lower bound on the size of arrays of strength t on those factors, and is no larger than L_k, the size of the complete factorial design. We investigate the relationship between the numbers L_t, and two questions in particular: For what t is L_t < L_k? And when L_t = L_k, is the complete factorial design the only array of that size and strength t? Arrays are assumed to be mixed-level.\n  We refer to an ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06558","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"}