For extra fun, you sometimes can make ideal filters with no false positives, if you know your possible elements ahead of time and you don't insert too many of t

For extra fun, you sometimes can make ideal filters with no false positives, if you know your possible elements ahead of time and you don't insert too many of them. (E.g., for 20 elements, you can construct a 12-bit code where there are guaranteed no false positives as long as you insert at most two elements.)