A t- \(\text {GHD}_k(s,v;\lambda )\) generalized Howell design is an \(s \times s\) array, each cell of which is either empty or contains a k-subset of elements of some set X of size v such that (i) each element of X appears exactly once in each row and in each column and (ii) no t-subset of elements from X appears in more than \(\lambda \) cells. Computer-aided classification of such designs is here considered in the framework of permutation codes with specific properties. Among other things, it is shown that a 2- \(\text {GHD}_3(7,18;1)\) exists and is unique; this settles the existence problem for 2- \(\text {GHD}_3(n+1,3n;1)\) .
