`GoldenSample` Incorrect about quasimontecarlo.jl HOT 4 CLOSED

Thanks, can you PR the fix and include a source? The lineage here seems to be SciML/Surrogates.jl#126 and #20, but there's no source. So it would be good to have that in the docstring.

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Thanks, can you PR the fix and include a source? The lineage here seems to be SciML/Surrogates.jl#126 and #20, but there's no source. So it would be good to have that in the docstring.

I can definitely add a source for using them in 1 or 2 dimensions, but there seem to be no references establishing the adequacy of these sequences in more than 2 dimensions, apart from a single blog post by a non-mathematician which contains no formal proofs.

There is, however, literature on using them in either 1 or 2 dimensions, where they're conjectured to have optimal properties. It's not at all clear the generalization in the blog post has these properties, and the sequences also appear to have exceedingly poor 2d projections. Here it is struggling with 8 dimensions and 64 points:

While Sobol has very little trouble:

And Faure handles it easily as well.

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Can you paste the links to these blog posts and such? This library needs to capture more of this kind of information in the docstrings (for all of the sampling methods 😅)

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In an extremely funny turn of events I have since learned about component-by-component constructions for QMC lattices. The original, buggy code probably produced better samples than the new "correct" code that follows the method laid out here.

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