Sequences with low discrepancy and pseudo-random numbers:theoretical results and numerical tests

Two methods of numerical integration in high or unbounded dimension are compared through both a theoretical and an experimental approach: the Monte Carlo method (using some (pseudo-) random numbers) and the quasi-Monte Carlo method (using some sequences with low discrepancy). A variant for the diaphony of the Koksma-Hlawka inequality is established. A multi-setting (smooth periodic, finite variation, dim-unbounded particle problem) testing methodology is processed on classical and new sequences.