Direct constructions for certain types of HMOLS Original Research Article

In this paper, we present 16 new types of three holey mutually orthogonal Latin squares (3-HMOLS for short) with equal-sized holes, along with 7 sets of 4-HMOLS, 2 sets of 6-HMOLS, and 34 sets of 7-HMOLS. We also provide some new sets of HMOLS that have n holes of size 2 and one hole of size 3.