  We study quasi-Monte Carlo integration in a weighted anchored Sobolev space.
As the underlying integration nodes we consider Halton sequences in prime bases
$\boldsymbol{p}=(p_1,\ldots,p_s)$ which are shifted with a
$\boldsymbol{p}$-adic shift based on $\boldsymbol{p}$-adic arithmetic. The
error is studied in the worst-case setting. In a recent paper, Hellekalek
together with the authors of this article proved optimal error bounds in the
root mean square sense, where the mean was extended over the uncountable set of
all possible $\boldsymbol{p}$-adic shifts. Here we show that candidates for
good shifts can in fact be chosen from a finite set and can be found by a
component-by-component algorithm.
