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The Optimal Isodual Lattice Quantizer in Three Dimensions

J. H. Conway·N. J. A. Sloane
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Abstract

The mean-centered cuboidal (or m.c.c.) lattice is known to be the optimal packing and covering among all isodual three-dimensional lattices. In this note we show that it is also the best quantizer. It thus joins the isodual lattices Z, A_2 and (presumably) D_4, E_8 and the Leech lattice in being simultaneously optimal with respect to all three criteria.

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J. H. Conway, N. J. A. Sloane. 2007-01-03. The Optimal Isodual Lattice Quantizer in Three Dimensions. https://arxiv.org/abs/math/0701080

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