If you read that paper you referenced, the Mersenne-Twister actually ended the Ferrenberg affair. And where does it say that lower bits of dSFMT are bad? Is there proof for this statement?
Now I am not saying that dSFMT is the best RNG ever, far from it. It's just very decent, and quite fast.
LCGs have an awkward habit of bad projections in 2D.
LCGs have an awkward habit of bad projections in 2D.