  High order perturbation theory has seen an unexpected recent revival for
controlled calculations of quantum many-body systems, even at strong coupling.
We adapt integration methods using low-discrepancy sequences to this problem.
They greatly outperform state-of-the-art diagrammatic Monte Carlo. In practical
applications, we show speed-ups of several orders of magnitude with scaling as
fast as $1/N$ in sample number $N$; parametrically faster than $1/\sqrt{N}$ in
Monte Carlo. We illustrate our technique with a solution of the Kondo ridge in
quantum dots, where it allows large parameter sweeps.
