With Simulation Any Method Goes?

Fallacy 8   You just choose whatever method you want to do simulation, there is no theoretical reason to prefer one over the other.

Counter Statement 8   There are theoretical reasons and discrepancy is one of the key measures in choosing one over another. Discrepancy is the best possible error bound. It is really part of the theory of integration with finite point sets.

Just as much as the error analysis of Riemann and Lebesgue Integrals, Discrepancy is a fundamental part of the theory of integration. So is the Variation of the function being integrated. The product of the Variation of the function and the Star Discrepancy is the error bound on any approximation of an integral by a finite set of points. This applies in any number of dimensions. The Koksma-Hlawka Inequality applies in any dimension and the Koksma Inequality applies in one dimension.