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：我们提出了一种用于精确计算机辅助构建具有已知对称群的格点沃罗诺伊胞的算法。该算法的计算复杂度优于随面总数线性增长，且适用于维度超过12的格点——这是先前方法无法实现的。我们将新算法应用于考克斯特-托德格点$K_{12}$以及通过层叠$K_{12}$得到的一系列格点族。通过优化该格点族，我们获得了新的13维最佳格点量化器（在已公布精确量化常数的格点中）。