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.

We study the sample median of independently generated quasi-Monte Carlo estimators based on randomized digital nets and prove it approximates the target integral value at almost the optimal convergence rate for various function spaces. In contrast to previous methods, the algorithm does not require a priori knowledge of underlying function spaces or even an input of pre-designed $(t,m,s)$-digital nets, and is therefore easier to implement. This study provides further evidence that quasi-Monte Carlo estimators are heavy-tailed when applied to smooth integrands and taking the median can significantly improve the error by filtering out the outliers.