{"paper":{"title":"Tractability properties of the weighted star discrepancy of the Halton sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Aicke Hinrichs, Friedrich Pillichshammer, Shu Tezuka","submitted_at":"2018-03-16T07:42:52Z","abstract_excerpt":"We study the weighted star discrepancy of the Halton sequence. In particular, we show that the Halton sequence achieves strong polynomial tractability for the weighted star discrepancy for product weights $(\\gamma_j)_{j \\ge 1}$ under the mildest condition on the weight sequence known so far for explicitly constructive sequences. The condition requires $\\sup_{d \\ge 1} \\max_{\\emptyset \\not= \\mathfrak{u} \\subseteq [d]} \\prod_{j \\in \\mathfrak{u}} (j \\gamma_j) < \\infty$. The same result holds for Niederreiter sequences and for other types of digital sequences. Our results are true also for the weig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06101","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"}