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

Exact calculation of quantizer constants for arbitrary lattices