Optimal length of supersequences over finite sets

Determine the optimal length of a supersequence containing every permutation of a set of n letters as a subsequence.

Background

A supersequence over a finite set is a sequence that contains every permutation of that set as a subsequence. The paper establishes that the minimum length for a set of eight letters is 52, thereby disproving the geometric Connell-sequence lower-bound conjecture, whose predicted value is 51.

For general set size n, the paper summarizes known asymptotic lower and upper bounds that remain separated. Determining the exact optimal length of such supersequences is therefore left unresolved.