The Voronoi Region of the Barnes-Wall Lattice Λ_16

01/15/2023

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by   Daniel Pook-Kolb, et al.

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We give a detailed description of the Voronoi region of the Barnes-Wall lattice Λ_16, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.