Paper 2026/2826
A Focus on Hermite Constant 11
, École Normale Supérieure - PSL, École Normale Supérieure - PSL, Fakultet inženjerskih nauka, Univerziteta u KragujevcuAbstract
This paper assembles the dimension-eleven argument in a series on the Hermite constants in dimensions ten, eleven and twelve. The root paper reduces a hypothetical lattice of minimum 4 and determinant below 972 to a chain of sections of ranks eleven, ten and nine. Its rank-nine section is marked by a perfect form below an explicit determinant cutoff. The global finite computation leaves 4 487 813 candidate forms and excludes all but ten by certificates. We state the mathematical content of these certificates, describe their data and checking rules, and prove why every valid certificate excludes the corresponding form. The four formats are trace, domain, glue and tree certificates; each tree must cover its entire stated domain. One of the ten remaining cases, 0052:005247066, is treated here by a complete gluing cover. Five companion papers settle the other nine. We also prove the common inequalities used by those local arguments. The resulting bound is $\gamma_{11}=4/\sqrt[11]{972}$, conditional on the attributed rank-nine classification, the rank-ten census and the stated global and local finite checks.
Note: Data on https://zenodo.org/records/23979316
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- LatticesHermiteLLL/BKZ output quality
- Contact author(s)
-
remi geraud @ ens fr
david naccache @ ens fr - History
- 2026-11-10: approved
- 2026-11-08: received
- See all versions
- Short URL
- https://ia.cr/2026/2826
- License
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CC BY
BibTeX
@misc{cryptoeprint:2026/2826,
author = {Rémi Géraud-Stewart and David Naccache},
title = {A Focus on Hermite Constant 11},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2826},
year = {2026},
url = {https://eprint.iacr.org/2026/2826}
}
