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We analyze the error introduced by approximately calculating the s-dimensional Lebesgue measure of a Jordan-measurable subset of I s = [0,1) s . We give an upper bound for the error of a method using a (t,m,s)-net, which is a set with a very regular distribution behavior. When the subset of I s is defined by some function of bounded variation on I s−1 ; the error is estimated by means of the variation of the function and the discrepancy of the point set which is used. A sharper error bound is established when a (t,m,s)-net is used. Finally a lower bound of the error is given, for a method using a (0,m,s)-net. The special case of the 2-dimensional Hammersley point set is discussed.

Error bounds for quasi-Monte Carlo integration with nets