{"paper":{"title":"A construction of (t,s)-sequences with finite-row generating matrices using global function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.CP"],"primary_cat":"math.NT","authors_text":"Harald Niederreiter, Roswitha Hofer","submitted_at":"2012-10-18T15:04:56Z","abstract_excerpt":"For any prime power $q$ and any dimension $s \\ge 1$, we present a construction of $(t,s)$-sequences in base $q$ with finite-row generating matrices such that, for fixed $q$, the quality parameter $t$ is asymptotically optimal as a function of $s$ as $s \\to \\infty$. This is the first construction of $(t,s)$-sequences that yields finite-row generating matrices and asymptotically optimal quality parameters at the same time. The construction is based on global function fields. We put the construction into the framework of $(u,{\\bf e},s)$-sequences that was recently introduced by Tezuka. In this wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5152","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"}