  Due to the curse of dimensionality, it is often prohibitively expensive to
generate deterministic space-filling designs. On the other hand, when using
na{\"i}ve uniform random sampling to generate designs cheaply, design points
tend to concentrate in a small region of the design space. Although, it is
preferable in these cases to utilize quasi-random techniques such as Sobol
sequences and Latin hypercube designs over uniform random sampling in many
settings, these methods have their own caveats especially in high-dimensional
spaces. In this paper, we propose a technique that addresses the fundamental
issue of measure concentration by updating high-dimensional distribution
functions to produce better space-filling designs. Then, we show that our
technique can outperform Latin hypercube sampling and Sobol sequences by the
discrepancy metric while generating moderately-sized space-filling samples for
high-dimensional problems.
