  In a recent paper Keister proposed two quadrature rules as alternatives to
Monte Carlo for certain multidimensional integrals and reported his test
results. In earlier work we had shown that the quasi-Monte Carlo method with
generalized Faure points is very effective for a variety of high dimensional
integrals occurng in mathematical finance. In this paper we report test results
of this method on Keister's examples of dimension 9 and 25, and also for
examples of dimension 60, 80 and 100. For the 25 dimensional integral we
achieved accuracy of 0.01 with less than 500 points while the two methods
tested by Keister used more than 220,000 points. In all of our tests, for n
sample points we obtained an empirical convergence rate proportional to n^{-1}
rather than the n^{-1/2} of Monte Carlo.
