Optimality and uniqueness of the Leech lattice among lattices
Metric Geometry
2017-08-23 v3
Abstract
We prove that the Leech lattice is the unique densest lattice in R^24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R^24 can exceed the Leech lattice's density by a factor of more than 1+1.65*10^(-30), and we give a new proof that E_8 is the unique densest lattice in R^8.
Cite
@article{arxiv.math/0403263,
title = {Optimality and uniqueness of the Leech lattice among lattices},
author = {Henry Cohn and Abhinav Kumar},
journal= {arXiv preprint arXiv:math/0403263},
year = {2017}
}
Comments
39 pages