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My question is probably worded incorrectly but here it is: I have (say) 3 discrete random variables: x1: has 15 levels (uniform pdf for simplicity) x2: has 3 levels (uniforms) x3: has 4 levels (uniform)

I want to generate n samples in such a way that:

  1. there are no repetitions of samples
  2. as n --> 15x3x4 the entire "full factorial" sample is generated;
  3. When generating (n+d) set of samples, the first n samples are the identical for any d

I tried to use Sobol quasi random sequence to generate this sample BUT I am not able to satisfy #1 above without retaining all prior points in memory and checking for duplicates. This is something I would like to avoid.

Thanks for your answers.

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if i have understood your question, then you might find my blog post on “how to do quasirandom fractional multi factorial sampling based on the sobol sequence.” useful.

http://extremelearning.com.au/a-probabilistic-approach-to-fractional-factorial-design/

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  • $\begingroup$ Welcome to the site. We are trying to build a permanent repository of high-quality statistical information in the form of questions & answers. Thus, we're wary of link-only answers, due to linkrot. Can you post a full citation & a summary of the information at the link, in case it goes dead? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jan 16, 2021 at 15:59

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