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# The optimal isodual lattice quantizer in three dimensions

• 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 $\mathbb Z$, $A_2$ and (presumably) $D_4, E_8$ and the Leech lattice in being simultaneously optimal with respect to all three criteria.
Mathematics Subject Classification: Primary: 52C07; Secondary: 11H55, 94A29.

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