  Stratified sampling is a fast and simple method to generate point sets with
uniform distribution in hypercubes. However, for the most common paraxial
stratfication it has the prominent drawback that the number of sampled points
in n dimensions has to be an n-th power of an integer number. This exponential
growth makes its application unattractive or even infeasible in high
dimensions. We present a stratification procedure that eliminates this problem
by a recursive binary partitioning of the hypercube. The algorithm runs in
linear time and tries to minimize the hyperboxes' deviation from the cubic
shape. We analyze the properties of the algorithm using discrepancy and
covering radius, and directly in practical applications, comparing it to
quasirandom and other sampling methods. We also discuss a potential combination
with Latin hypercube sampling, which positively affects discrepancy.
