We introduce a novel method to generate sample sequences that are progressively stratified
both in high dimensions and in lower-dimensional projections. Our method comes from a
new observation that Owen-scrambled quasi-Monte Carlo (QMC) sequences can be
generated as stratified samples, merging the QMC construction and random scrambling into
a stochastic algorithm. This yields simpler implementations of Owen-scrambled Sobol',
Halton, and Faure sequences that exceed the previous state-of-the-art sample-generation …