  In this paper we establish the sharp rate of the optimal dual quantization
problem. The notion of dual quantization was recently introduced in the paper
[8], where it was shown that, at least in an Euclidean setting, dual quantizers
are based on a Delaunay triangulation, the dual counterpart of the Voronoi
tessellation on which "regular" quantization relies. Moreover, this new
approach shares an intrinsic stationarity property, which makes it very
valuable for numerical applications. We establish in this paper the counterpart
for dual quantization of the celebrated Zador theorem, which describes the
sharp asymptotics for the quantization error when the quantizer size tends to
infinity. The proof of this theorem relies among others on an extension of the
so-called Pierce Lemma by means of a random quantization argument.
