  We show how information on the uniformity properties of a point set employed
in numerical multidimensional integration can be used to improve the error
estimate over the usual Monte Carlo one. We introduce a new measure of
(non-)uniformity for point sets, and derive explicit expressions for the
various entities that enter in such an improved error estimate. The use of
Feynman diagrams provides a transparent and straightforward way to compute this
improved error estimate.
