  For uniform scalar quantization, the error distribution is approximately a
uniform distribution over an interval (which is also a 1-dimensional ball).
Nevertheless, for lattice vector quantization, the error distribution is
uniform not over a ball, but over the basic cell of the quantization lattice.
In this paper, we construct vector quantizers with periodic properties, where
the error is uniformly distributed over the n-ball, or any other prescribed
set. We then prove upper and lower bounds on the entropy of the quantized
signals. We also discuss how our construction can be applied to give a
randomized quantization scheme with a nonuniform error distribution.
