Can I reverse any hash algorithms to find a set of the possible orginals? If I map 1024 bits onto a 16 bit hash (just random numbers for conversation sake), I will have an average of 64 collisions per hash (assuming a good algorithm). I wonder if anyone knows any hash algorithms around today in which I could take a hash and extrapolate the ~64 1024 bit original values? I suppose that's not easy, but I don't know for sure. My thought process is to see if I could tack an index number onto the end of the hash to enable me to extrapolate the original (perhaps at a significant cpu cost) later.

If your hash is only 16 bits, then on average there will be $2^{1008}$ different possible preimages for any hash value. It may be that you're only using 64 of those in practice, but you can't identify those _from the hash_ alone, without using (very strong) additional information about the distribution of the actually occurring values.