  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 this, we obtain an expression for the
covariance of the integral estimator in terms of the Walsh coefficients of the
function. Finally, we prove that the covariance of the integral estimator is
negative when the Walsh coefficients of the function satisfy a certain decay
condition. To do this, we use creative telescoping and recurrence solving
algorithms from symbolic computation to find a sign equivalent closed form
expression for the covariance term.
