  Antithetic sampling, which goes back to the classical work by Hammersley and
Morton (1956), is one of the well-known variance reduction techniques for Monte
Carlo integration. In this paper we investigate its application to digital nets
over $\mathbb{Z}_b$ for quasi-Monte Carlo (QMC) integration, a deterministic
counterpart of Monte Carlo, of functions defined over the $s$-dimensional unit
cube. By looking at antithetic sampling as a geometric technique in a compact
totally disconnected abelian group, we first generalize the notion of
antithetic sampling from base $2$ to an arbitrary base $b\ge 2$. Then we
analyze the QMC integration error of digital nets over $\mathbb{Z}_b$ with
$b$-adic antithetics. Moreover, for a prime $b$, we prove the existence of good
higher order polynomial lattice point sets with $b$-adic antithetics for QMC
integration of smooth functions in weighted Sobolev spaces. Numerical
experiments based on Sobol' point sets up to $s=100$ show that the rate of
convergence can be improved for smooth integrands by using antithetic sampling
technique, which is quite encouraging beyond the reach of our theoretical
result and motivates future work to address.
