Generating "dependent" quasi-random numbers

Under certain conditions on the integrand, quasi-Monte Carlo methods for estimating integrals (expectations) converge faster asymptotically than Monte Carlo methods. Motivated by this result, we consider the generation of quasi-random vectors with given marginals and given correlation matrix. We extend the "Normal To Anything" (NORTA) method, introduced by M.C. Cario and B.L. Nelson (1997), to this context, and term the extension the "Quasi-Random to Anything" (QUARTA) method.