Funtion or something that finds the smaller integer

Apologies Kosh271 but it looks you misunderstood the problem. The issue raised was about the huge logic and coding needed for checking 256 words and it was not about timing (yet). Your solution comes with even more registers amounting to several thousands for a simple job let alone the amount of coding and logic involved.

If the 256 data words can be streamlined (and they should be) then you don't need anything like memory or logic apart from the simple algorithm that I mentioned. Run the stream through one comparator and update final result to contain the smallest integer. Then apply reset and restart for a new stream.