Minimum sums of moments or, equivalently, distorsion of optimum quantizers play an important role in several branches of mathematics. Fejes Tóth’s inequality for sums of moments in the plane and Zador’s asymptotic formula for minimum distortion in Euclidean d-space are the first precise pertinent results in dimension d ≥ 2. In this article these results are generalized in the form of asymptotic...