{
  "abstract": "We study the normalized discrepancy in the Luxemburg norm generated by $Φ(s)=s\\log(1+s)$. For arbitrary nonnegative quadrature weights, we prove that the associated information complexity suffers from the curse of dimensionality: for every $\\varepsilon\\in(0,1)$, there exist constants $c_\\varepsilon>0$ and $d_0=d_0(\\varepsilon)\\in\\mathbb{N}$ such that \\[N_{Φ,+}(\\varepsilon,d)\\ge c_{\\varepsilon} d^{-1}(1.07735\\ldots)^d \\qquad \\mbox{for all } d\\ge d_0. \\] The result therefore also applies to equal-weight quasi-Monte Carlo rules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21717",
  "author_total": 2,
  "authors": [
    {
      "name": "Josef Dick"
    },
    {
      "name": "Friedrich Pillichshammer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/as9a36v91dhe6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21717",
  "fulltext_url": null,
  "id": "as9a36v91dhe6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21717",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
    ]
  ],
  "openalex": "W7222753969",
  "pdf_url": "https://arxiv.org/pdf/2610.21717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/as9a36v91dhe6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "The $L\\log L$-Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality",
  "title_text": "The Llog L-Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/as9a36v91dhe6",
  "venue": "arXiv",
  "versions": []
}