I was thinking about LCG generators with modulus 2^16 (16 bits of state). I know that good multipliers for 32-bit (and bigger) LCGs can be found in
L'ecuyer and Vigna's papers.
So we got: 43317, 47989, 64733, 8477, right? By the way can you give me an example of bad ones? I know that 3 and 5 would be bad, but I need less obvious examples. I should probably say that they should have a high Kolmogorov complexity, but I can't precisely define it - so let's say I'm looking for bad ones, that look random (although I know that this is a imprecise criterion).
By the way I was thinking also about golden ratio (times 2^16), I read somewhere that such a multiplier is good for hashing, is it reasonable to assume that it will have a good spectral score for LCG mod 2^n (I mean golden ratio times 2^n as a multiplier). In case of 16-bit LCG it would be 40503.