Glued Lattices Are Better Quantizers Than K_12
Agrell Erik, Pook-kolb Daniel, Allen Bruce. Arxiv 2023
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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