Existence of three HMOLS of types hn and 2n31 Original Research Article

In this paper, we construct 23 new 3 HMOLS of type hn. We also investigate the existence of 3 HMOLS of type 2n31 and show that the necessary condition n ⩾ 6 is sufficient for such designs to exist except possibly for 18 values of n, of which n = 31 is the largest. As an application, some improvements for the existence of perfect Mendelsohn designs with block size five are also mentioned.