  We develop a randomized algorithm (that succeeds with high probability) for
generating an $\epsilon$-net in a sphere of dimension n. The basic scheme is to
pick $O(n \ln(1/n) + \ln(1/\delta))$ random rotations and take all possible
words of length $O(n \ln(1/\epsilon))$ in the same alphabet and act them on a
fixed point. We show this set of points is equidistributed at a scale of
$\epsilon$. Our main application is to approximate integration of Lipschitz
functions over an n-sphere.
