Sobol uses initial polynome to generate unform across one dimension. In d dimension, there are d Sobol generators (determined by d polynomes of initilization). However, Sobol has flaws. The graph you shown is valid only a lower dimensions.

Jun 24, 2016 · Therefore I am investigating scrambled Sobol sequences, and I am looking for an easy to code approach. The method described in "On the scrambled sobol sequence" by Chi, Beerli, Evan, Mascagni (2005) seems simple enough from a coding point of view, however I don't understand how it is supposed to work.

Jun 28, 2018 · If Sobol is just a type of sequence, perhaps this can be adapted into one with all the same properties - it's much more straightforward to calculate so it would make a good substitute. sequences-and-series

Beyond just making the program work, I would like to learn the mathematics behind the Sobol sequence (and other quasi-random sequences). I understand that the Sobol sequence is based on finite field, but I have not found any introductory finite field book with applications on quasi-random sequence.