Variance and discrepancy with alternative scramblings

This paper analyzes some schemes for reducing the computational burden of digital scrambling. Some such schemes have been shown not to affect the mean squared L 2 discrepancy. This paper shows that some discrepancy-preserving alternative scrambles can change the variance in scrambled net quadrature. Even the rate of convergence can be adversely affected by alternative scramblings. Finally, some alternatives reduce the computational burden and can also be shown to improve the rate of convergence for the variance, at least in dimension 1.