  One of the fundamental problem in the theory of sorting is to find the
pessimistic number of comparisons sufficient to sort a given number of
elements. Currently 16 is the lowest number of elements for which we do not
know the exact value. We know that 46 comparisons suffices and that 44 do not.
There is an open question if 45 comparisons are sufficient. We present an
attempt to resolve that problem by performing an exhaustive computer search. We
also present an algorithm for counting linear extensions which substantially
speeds up computations.
