Glued Lattices Are Better Quantizers Than K_12

Agrell Erik, Pook-kolb Daniel, Allen Bruce. Arxiv 2023

[Paper]    
ARXIV Quantisation

40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice $K_{12}$ for quantization, and estimated its second moment. Since then, all published lists identify $K_{12}$ as the best 12-dimensional lattice quantizer. Surprisingly, $K_{12}$ 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.

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