Dimension-independent convergence rates of randomized nets using median-of-means

Abstract: Recent advances in quasi-Monte Carlo integration demonstrate that the median of linearly scrambled digital net estimators achieves near-optimal convergence rates for high-dimensional integrals without requiring a priori knowledge of the integrand's smoothness. Building on this framework, we prove that the median estimator attains dimension-independent convergence under tractability conditions characterized by low effective dimensionality, a property known as strong tractability in complexity theory. Our analysis strengthens existing guarantees by improving the convergence rates and relaxing the theoretical assumptions previously required for dimension-independent convergence.