I have been using Sobol for Montecarlo pricing. I noticed something that surprised me, I try to explain it with some details.Let us say that for a simulation I need 10,000 points in the n-dimensional cube. I use the first 10,000 points in the Sobol sequence (now don't worry about and initial offset), obtained with sobolset command in Matlab, and get a result r0. I can do it again with the following 10,000 points in the Sobol sequence and obtain a different result r1, etc. The point is that r_i and r_{i+1} don't seem to be independent at all. In fact, when I plot one against the other, I observe interesting patterns of points, covering a tiny part of the [0,1]^2 square. Of course I know we get something like that when plotting the ith against the jth coordinate of the sobol sequence, specially for high values of i and j, but now I am plotting a function of shifted positions in the sobol sequence. For instance, if I just plot e_{i+1} against e_{i}, where e_i is the first (or any fixed) coordinate of the ith point in the Sobol sequence, I also get those patterns.I thought this was to be expected, and that the scrambling methods (like the one called 'MatousekAffineOwen') were just designed to make those patterns dissapear, and render a more or less homogeneous cloud in the square [0,1]^2. But that does not seem to be the case: I got other (arguably more disperse) patterns of points. But ugly nevertheless, and with high Pearson Correlation, not close to zero as I would have expected. So I decided to perform a final experiment. I tried my own naive scrambling, chose two largish primes p, q, and used the elements in sobol: Sim(n) = Sobol( (p^n) mod q ).Then I plotted the same and now there is no trace of point patterns, and Pearson's Corr. is nicely close to zero.So, what I am missing? Isn't the normal "MatoukAffineOwen" scrambling dangerous in this context? Otherwise, what is the advantage of using it? Thank you in advance,

Thanks a lot, I'll give it a try.

Hello klp2Can you exactly describe your experiment and eventually post a chart where you notice some dependence between the first 1-10000 and the next 10001-20000 Sobol numbers ? In which dimension are you working ?I have two Sobol generators (each implemented with a different algorithm) and can try to reproduce/explain your results.