  Optimal gap sequences in Shellsort, defined as gap sequences having the
minimised maximum number of comparisons for a fixed number of pairwise distinct
elements, are found by minimax search in reduced permutational spaces, namely
Bad $(s,1)$-sorted permutations. Exact optimal gap sequences in Shellsort for
$n\leq16$ pairwise distinct elements are established, and the best known gap
sequences for $17\leq n\leq 30$ are listed with conjectures made. It notably
discovers some optimal gap sequences consist of increments larger than the half
of the total number of the elements to sort.
