That answers the question of how many bits of pi we know. If you want to be able to take an arbitrary n-bit string and find its position in a set of n-bit strin

That answers the question of how many bits of pi we know. If you want to be able to take an arbitrary n-bit string and find its position in a set of n-bit strings, you need to have something like 2^n strings in your set. So to find the number of bits you can support for an algorithm like this, taking the log of the number of digits of pi we know gives you a rough estimate.