How to restore default seed generation in SeedRandom[] when specifying method?

Question

I want to generate low-discrepancy sequences and for that purpose I use SeedRandom[], like:

BlockRandom[
   SeedRandom[(* ..., *) Method -> {"MKL", Method -> {"Sobol", "Dimenstion"->2}}];
RandomReal[1,10]]

The problem is that RandomReal[] returns the same sequence always as if I set the seed to some fixed number.

My question is: what should I put as argument to SeedRandom[] in order to restore the default behaviour or how could I change the method without affecting the way the generator is seeded ?

EDIT: One work-around would be to calculate a bunch of seeds with, say, seeds = RandomInteger[2^32] before calling SeedRandom[] for the 1st time and subsequently feed them to the latter.

Answer 1

If you put SeedRandom[], the seed will be reset using the time of day. This gives a new starting point to the random generator at the time of execution. One can use SeedRandom[Method -> ...] to set the method first, if desired.

Example:

BlockRandom[
  SeedRandom[Method -> {"MKL", Method -> {"Sobol", "Dimension"->2}}];
  SeedRandom[];
  RandomReal[1,10]]

Answer 2

You can use SeedRandom without the first argument to change the method (without changing the way it is seeded) by specifying only the Method (and not the actual seed). For example:

SeedRandom[Method -> "Congruential"]
RandomReal[{0, 1}, {10, 10}]

SeedRandom[Method -> "ExtendedCA"]
RandomReal[{0, 1}, {10, 10}]