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.

翻译：40年前，Conway和Sloane提出使用高度对称的Coxeter-Todd格点$K_{12}$进行量化，并估计了其二阶矩。此后，所有已发表的列表均将$K_{12}$列为最佳12维格点量化器。令人惊讶的是，$K_{12}$并非最优：我们通过构造两个新的12维格点，获得了更低的归一化二阶矩。这些新格点是通过将6维格点粘合在一起而得到的。