Exact calculation of quantizer constants for arbitrary lattices
Daniel Pook-Kolb, Bruce Allen, Erik Agrell
我们提出了一个算法,用于用已知对称组的晶格的Voronoi细胞的精确计算机辅助构建。 我们的算法与人脸总数相比,在线方面比线性缩放要好,并且适用于12以外的尺寸,这是以前的方法无法实现的。 新算法应用于Coxeter-Todd 格子K_12以及从层压K_12获得的晶格家族。 通过优化这个家族,我们获得了一个新的13维格位,其量子化常数比提交时的任何已发表的都小。 (关于后续改进,请参阅在结论后添加的注释。
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 13-dimensional lattice, whose quantizer const...