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Agrell, Erik; Pook-Kolb, Daniel; Allen, Bruce
IEEE transactions on information theory, 05/2024Journal Article
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 products of two 6-dimensional lattices.
