  Quasi-Monte Carlo methods replaced classical Monte Carlo methods in many
areas of numerical analysis over the last decades. The purpose of this paper is
to extend quasi-Monte Carlo methods into a new direction. We construct and
implement a uniformly distributed sequence in the orthogonal group O(n). From
this sequence we obtain a uniformly distributed sequence on the Grassmannian
manifold $G(n,k)$, which we use to approximate integral-geometric formulas. We
show that our algorithm compares well with classical random constructions and,
thus, motivate various directions for future research.
