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The optimal four-dimensional lattice quantizer and bounds from Voronoi facets — arXiv:2611.00100

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00100
License (as archived): CC0-1.0
Archived: 2026-11-03T18:50:46.887Z
SHA-256 of the archived text: 7463869495c8ba8ed88813da4430e5e31e283fa0ecbb224140d9f2d3ee69d5e3
Stable URL of this page: https://metraipolis.com/documento/dc_fc9abebcf494

How to cite

The optimal four-dimensional lattice quantizer and bounds from Voronoi facets — arXiv:2611.00100 — arXiv (en), https://arxiv.org/abs/2611.00100 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fc9abebcf494 (Metraipolis archive dc_fc9abebcf494, sha256 7463869495c8ba8ed88813da4430e5e31e283fa0ecbb224140d9f2d3ee69d5e3)

BibTeX

@misc{dcfc9abebcf494,
  title = {The optimal four-dimensional lattice quantizer and bounds from Voronoi facets — arXiv:2611.00100},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00100},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fc9abebcf494; sha256 7463869495c8ba8ed88813da4430e5e31e283fa0ecbb224140d9f2d3ee69d5e3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00100. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove that the root lattice $D_4$ uniquely minimizes the normalized second moment among four-dimensional lattices, up to similarity. The computer-assisted proof combines the classification of secondary cones with integration over Voronoi cells and weighted sums of squares. In dimensions at least two, comparison with circular cones gives a lower bound in terms of the number of Voronoi facets, improving the sphere bound and recovering the hexagonal value in dimension two. We prove Ajjanagadde's circular-cone concavity conjecture and deduce the lattice case of his conjectured quantization bound.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Metric Geometry (math.MG) ; Information Theory (cs.IT); Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.00100 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:15:38.111Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).