Additional Dimensions for the Sobol Generator

[linas@austin.ibm.com]

On Tue, Apr 06, 2004 at 11:15:06AM +0200, Philipp No?l Baecker wrote:
> Dear Group:
>  
> Some time ago there was a discussion about increasing the dimensionality of
> the Sobol QRNG. Today I came across an article by Joe and Kuo (2003) and
> added the additional primitive polynomials and direction numbers reported in
> their article. I did not thoroughly check them but will do so in a couple of
> days. Information on the quality of the sequences generated would be highly
> appreciated.


> static const int primitive_polynomials[MYSOBOL_MAX_DIMENSION] = 
...
> 3743, 3747, 3771, 3791, 3805, 3827, 3833, 3851, 3865, 3889, 3895, 3933,
> 3947, 3949, 3957, 3971, 3985, 3991, 3995, 4007, 4013, 4021, 4045, 4051,
...

Ughhh.  I hope you didn't type these in by hand?  Hopefully, you have
some 'simple' algorithm, e.g. some perl script, for generating these 
polynomials.  Then verifying the correctness of the poly's is a 
matter of verifying the correctness of the perl script.  Otherwise,
you could die of fright looking for a typo in that table of numbers.
(Hopefully Joe & Kuo gave an algo to generate these?)

disclaimer: I know nothing about sobol or qrng.  The above is just a 
'style' comment.

--linas