{"paper":{"title":"Optimal order of $L_p$-discrepancy of digit shifted Hammersley point sets in dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aicke Hinrichs, Friedrich Pillichshammer, Ralph Kritzinger","submitted_at":"2014-10-16T07:08:00Z","abstract_excerpt":"It is well known that the two-dimensional Hammersley point set consisting of $N=2^n$ elements (also known as Roth net) does not have optimal order of $L_p$-discrepancy for $p \\in (1,\\infty)$ in the sense of the lower bounds according to Roth (for $p \\in [2,\\infty)$) and Schmidt (for $p \\in (1,2)$). On the other hand, it is also known that slight modifications of the Hammersley point set can lead to the optimal order $\\sqrt{\\log N}/N$ of $L_2$-discrepancy, where $N$ is the number of points. Among these are for example digit shifts or the symmetrization. In this paper we show that these modified"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4315","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"}