  A supersequence over a finite set is a sequence that contains as subsequence
all permutations of the set. This paper defines an infinite array of methods to
create supersequences of decreasing lengths. This yields the shortest known
supersequences over larger sets. It also provides the best results
asymptotically. It is based on a general proof using a new property called
strong completeness. The same technique also can be used to prove existing
supersequences which combines the old and new ones into an unified conceptual
framework.
