  Quasi-Monte Carlo rules are equal weight quadrature rules defined over the
domain $[0,1]^s$. Here we introduce quasi-Monte Carlo type rules for numerical
integration of functions defined on $\mathbb{R}^s$. These rules are obtained by
way of some transformation of digital nets such that locally one obtains qMC
rules, but at the same time, globally one also has the required distribution.
We prove that these rules are optimal for numerical integration in fractional
Besov type spaces. The analysis is based on certain tilings of the Walsh phase
plane.
