  We study high-dimensional numerical integration in the worst-case setting.
The subject of tractability is concerned with the dependence of the worst-case
integration error on the dimension. Roughly speaking, an integration problem is
tractable if the worst-case error does not explode exponentially with the
dimension. Many classical problems are known to be intractable. However,
sometimes tractability can be shown. Often such proofs are based on randomly
selected integration nodes. Of course, in applications true random numbers are
not available and hence one mimics them with pseudorandom number generators.
This motivates us to propose the use of pseudorandom vectors as underlying
integration nodes in order to achieve tractability. In particular, we consider
digital inverse vectors and present two examples of problems, the weighted star
discrepancy and integration of H\"older continuous, absolute convergent
Fourier- and cosine series, where the proposed method is successful.
