[Jump to code hierarchy]

Universally optimal sphere packing[1]

Description

A periodic sphere packing that (weakly) minimizes all completely monotonic potentials of square Euclidean distance among all periodic packings of the same density.

Member of code lists

Primary Hierarchy

Classical Domain
Analog Kingdom
Analog codeECC
Sphere packing
Parents
Sphere packing
Universally optimal codeECC
Universally optimal sphere packing
Children
\(E_8\) Gosset lattice
The \(E_8\) Gosset lattice is universally optimal [2].
\(\Lambda_{24}\) Leech lattice
The Leech lattice is universally optimal [2].
\(A_2\) triangular lattice
The triangular lattice is universally optimal among lattices [3] and among all planar configurations of the same density [4].

References

[1]
H. Cohn and A. Kumar, “Universally optimal distribution of points on spheres”, Journal of the American Mathematical Society 20, 99 (2006) arXiv:math/0607446 DOI
[2]
H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, and M. Viazovska, “Universal optimality of the \(E_8\) and Leech lattices and interpolation formulas”, (2022) arXiv:1902.05438
[3]
H. L. Montgomery, “Minimal theta functions”, Glasgow Mathematical Journal 30, 75 (1988) DOI
[4]
OpenAI, “Universal optimality of the triangular lattice”, preprint (2026) URL
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

— see instructions

Zoo Code ID: univ_opt_analog

Cite as:
“Universally optimal sphere packing”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/univ_opt_analog, arXiv:2606.11484
BibTeX:
@incollection{eczoo_univ_opt_analog,
title={Universally optimal sphere packing},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/univ_opt_analog}
}
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/univ_opt_analog

Cite as:

“Universally optimal sphere packing”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/univ_opt_analog, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/analog/sphere_packing/univ_opt_analog.yml.