Simplistically put, using a random, Monte Carlo style algorithm, but deterministically, by sampling at well-chosen points.
Key words: discrepancy.
Some of the series of points used are nice for parallelised algorithms, by the way, in the same way that randomised algorithms are.
Low discrepancy sequences such as Sobol nets, Gray codes, others? If you aren't doing this incrementally you can pre-generate a point set rather than a sequence.
Quasi Monte Carlo introduction by Sasha Nikolov
Practical example: Generating Hammersley point sets for image synthesis.
Dirk Nuyens' magic point shop contains “QMC point generators and generating vectors” (MATLAB/octave/C++)