# Walsh functions, scrambled $(0, m, s)$-nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration

@article{Wiart2021WalshFS, title={Walsh functions, scrambled \$(0, m, s)\$-nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration}, author={Jaspar Wiart and Elaine Wong}, journal={Math. Comput. Simul.}, year={2021}, volume={182}, pages={277-295} }

Abstract We investigate base b Walsh functions for which the variance of the integral estimator based on a scrambled ( 0 , m , s ) -net in base b is less than or equal to that of the Monte-Carlo estimator based on the same number of points. First we compute the Walsh decomposition for the joint probability density function of two distinct points randomly chosen from a scrambled ( t , m , s ) -net in base b in terms of certain counting numbers and simplify it in the special case t is zero. Using… Expand

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