Downward coordinate compression
= Downward coordinate compression
In a <set family>, replace a set containing $i$ by its deletion of $i$ only when that deletion is absent. This preserves cardinality and cannot increase maximum pairwise <Hamming distance>. If a new set and a retained set gave a larger distance, the retained set's deletion would already have been present; that deletion and the original uncompressed set would give the same distance. Repeated downward compressions yield a <down-set>.