I recently stumbled upon this problem. Naively I thought that any transformation from uniform would work, so I plugged in a 1D Sobol (and Halton) sequence as if the sequence where a random number generator into an [`std::normal_distribution<>`][1] variate. To my surprise it didn't work, it obviously generated a non normal distribution. 

Ok, then I took the Numerical Recipes Third Edition Chapter 7.3.9 `Normal_dev` function to generate normal numbers from the Sobol or Halton sequences by the method of "Ratio-of-Uniforms" and it failed in the same way. Then I though, ok, if you look at the code, it takes two uniform random numbers to generate two normally distributed random numbers. Perhaps if I used a Sobol (or Halton) 2D sequence it will work. Well, it failed again.

The I remembered about the ["Box-Muller method"][2] (mentioned in the comments) and since it has a more geometric interpretation then I though it could work. Well, it did work! I was very excited an starting doing other test, the distribution looks normal.

The problem I saw was that the distribution was no better than random, it terms of filling, so I was a bit disappointed, but ready to publish the result.

Then I did a deeper search (now that I knew what to look for), and it turn out that there is already a paper on this subject: http://www.sciencedirect.com/science/article/pii/S0895717710005935

In this paper it is actually claimed 

> Two well known methods used with pseudorandom numbers are the
> Box–Muller and the inverse transformation methods. Some researchers
> and financial engineers have claimed that it is incorrect to use the
> Box–Muller method with low-discrepancy sequences, and instead, the
> inverse transformation method should be used. In this paper we prove
> that the Box–Muller method can be used with low-discrepancy sequences,
> and discuss when its use could actually be advantageous.

So the overall conclusion is this:

1) You can use the Box-Muller on 2D low discrepancy sequences to obtain normally distributed sequences. But the low discrepancy/space filling properties seem to be lost.

2) You can use the inverse method, presumably the low discrepancy/space filling properties will be preserved.

3) Ratio-of-Uniforms cannot be used.

EDIT: This http://mathoverflow.net/a/144234 points to the same conclusions.

I made an illustration:

[![figures][3]][3]


  [1]: http://en.cppreference.com/w/cpp/numeric/random/normal_distribution
  [2]: https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
  [3]: https://i.sstatic.net/4HJIp.png