Glued lattices are better quantizers than $K_{12}$
Information Theory
2024-06-25 v3 Mathematical Physics
math.IT
Metric Geometry
math.MP
Abstract
40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice for quantization, and estimated its second moment. Since then, all published lists identify as the best 12-dimensional lattice quantizer. Surprisingly, is not optimal: we construct two new 12-dimensional lattices with lower normalized second moments. The new lattices are obtained by gluing together 6-dimensional lattices.
Cite
@article{arxiv.2312.00481,
title = {Glued lattices are better quantizers than $K_{12}$},
author = {Erik Agrell and Daniel Pook-Kolb and Bruce Allen},
journal= {arXiv preprint arXiv:2312.00481},
year = {2024}
}