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Smith \(40\)-point code[1,2]

Description

A \((10,40,1/6)\) spherical code found by W. D. Smith [1] and conjectured to be optimal in terms of minimizing potential energy functions [2]. A beautified set of coordinates can be found on the site [1].

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Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy spherical codeECC
Spherical code
Parents
Spherical code
Smith \(40\)-point code

References

[1]
N. J. A. Sloane, R. H. Hardin, and W. D. Smith, “Tables of spherical codes”, (2004) URL
[2]
B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, “Experimental Study of Energy-Minimizing Point Configurations on Spheres”, Experimental Mathematics 18, 257 (2009) arXiv:math/0611451 DOI
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Zoo Code ID: smith_spherical

Cite as:
“Smith \(40\)-point code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/smith_spherical, arXiv:2606.11484
BibTeX:
@incollection{eczoo_smith_spherical,
title={Smith \(40\)-point code},
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/smith_spherical}
}
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Permanent link:
https://errorcorrectionzoo.org/c/smith_spherical

Cite as:

“Smith \(40\)-point code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/smith_spherical, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/sharp_config/smith_spherical.yml.