  We use the framework of dependence to assess the benefits of scrambling
randomly versus deterministically for Faure and Halton sequences. We attempt to
answer the following questions: when a deterministic sequence has known defects
for small sample sizes, should we address these defects by applying random
scrambling or should we find a "good" deterministic scrambling yielding a
sequence that can then be randomized using a less computer-intensive
randomization method such as a digital shift? And in the latter case, how do we
choose a deterministic scrambling and how do we assess whether it is good or
not?
