The Optimal Isodual Lattice Quantizer in Three Dimensions
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, A2 and (presumably) D4, E8 and the Leech lattice in being simultaneously optimal with respect to all three criteria.
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