How can k permutations on n-set be arranged to maximize minimal pairwise Kendall tau distance (i.e. number of discordant pairs) between them?

For two permutations this is obviously when the second permutation is the reverse of the first one, with distance $n(n-1)/2$, but what about larger $k$?

Update: The main question is the asymptotic of normalized (by the factor $n(n-1)/2$) distance when $n \rightarrow \infty$.