  We consider the problem of computing an approximation to the integral
$I=\int_{[0,1]^d}f(x) dx$. Monte Carlo (MC) sampling typically attains a root
mean squared error (RMSE) of $O(n^{-1/2})$ from $n$ independent random function
evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully
equispaced evaluation points can attain the rate $O(n^{-1+\varepsilon})$ for
any $\varepsilon>0$ and randomized QMC (RQMC) can attain the RMSE
$O(n^{-3/2+\varepsilon})$, both under mild conditions on $f$. Classical
variance reduction methods for MC can be adapted to QMC. Published results
combining QMC with importance sampling and with control variates have found
worthwhile improvements, but no change in the error rate. This paper extends
the classical variance reduction method of antithetic sampling and combines it
with RQMC. One such method is shown to bring a modest improvement in the RMSE
rate, attaining $O(n^{-3/2-1/d+\varepsilon})$ for any $\varepsilon>0$, for
smooth enough $f$.
