The Optimal Lattice Quantizer in Three Dimensions*

E. S. Barnes
Department of Pure Mathematics
The University of Adelaide
Adelaide, S.A. 5001, Australia

N. J. A. Sloane**
AT&T Labs - Research 
Murray Hill, New Jersey 07974, USA


* A slightly different version of this paper appeared in
  SIAM J. Algebraic Discrete Methods},
  4 (No. 1, March 1983), 30--41.

** Current address: AT\&T Shannon Labs, 180 Park Avenue,
   Florham Park, NJ 07932--0971


ABSTRACT

The body-centered cubic lattice is shown to have the
smallest mean squared error of any lattice quantizer
in three dimensions, assuming that the input to the
quantizer has a uniform distribution.

For the full version, see:
http://www.research.att.com/~njas/doc/optimal.pdf
or
http://www.research.att.com/~njas/doc/optimal.ps