We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond 12, which previous methods could not achieve. The new algorithm is applied to the Coxeter-Todd lattice $K_{12}$ as well as to a family of lattices obtained from laminating $K_{12}$. By optimizing this family, we obtain a new best 13-dimensional lattice quantizer (among the lattices with published exact quantizer constants).

翻译：我们提出一种算法，用于在已知对称群条件下精确构建格点Voronoi胞的计算机辅助构造。该算法的时间复杂度优于与总面数呈线性关系，并能应用于维度超过12的格点——这是此前方法无法实现的。我们将新算法应用于Coxeter-Todd格点$K_{12}$，以及通过对$K_{12}$进行层叠得到的一类格点族。通过优化该格点族，我们在已公布精确量化器常数的格点中，获得了新的13维最佳格点量化器。