Welcome to the resource topic for 2022/677
Title:
A Conjecture on Hermite Constants
Authors: Leon Mächler and David Naccache
Abstract:As of today, the Hermite constants \gamma_n are only known for n\in \{1,2,3,4,5,6,7,8,24\}. We noted that the known values of (4/\gamma_n)^n coincide with the values of the minimal determinants of any n-dimensional integral lattice when the length of the smallest lattice element \mu is fixed to 4. Based on this observation, we conjecture that the values of \gamma_n^n for n=9,\ldots,23 are those given in Table 2. We provide a supporting argument to back this conjecture. We also provide a provable lower bound on the Hermite constants for 1\leq n\leq24.
ePrint: https://eprint.iacr.org/2022/677
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .