{"paper":{"title":"Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Friedrich Pillichshammer, Mario Neum\\\"uller","submitted_at":"2016-05-02T07:47:12Z","abstract_excerpt":"The star discrepancy $D_N^*(\\mathcal{P})$ is a quantitative measure for the irregularity of distribution of a finite point set $\\mathcal{P}$ in the multi-dimensional unit cube which is intimately related to the integration error of quasi-Monte Carlo algorithms. It is known that for every integer $N \\ge 2$ there are point sets $\\mathcal{P}$ in $[0,1)^d$ with $|\\mathcal{P}|=N$ and $D_N^*(\\mathcal{P}) =O((\\log N)^{d-1}/N)$. However, for small $N$ compared to the dimension $d$ this asymptotically excellent bound is useless (e.g. for $N \\le {\\rm e}^{d-1}$).\n  In 2001 it has been shown by Heinrich, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00378","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"}