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Existence of three HMOLS of types hn and 2n31

F.E. Bennett, C.J. Colbourn, L. Zhu
1996 Discrete Mathematics  
We also investigate the existence of 3 HMOLS of type 2"31 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  ...  In this paper, we construct 23 new 3 HMOLS of type h".  ...  Acknowledgements This research was supported in part by NSERC grant A5320 and a grant from the Mount Saint Vincent University Committee on Research and Publications to the first author.  ... 
doi:10.1016/0012-365x(95)00148-p fatcat:lyq7yhs7vfc63ot4ubc7vjitg4

Direct constructions for certain types of HMOLS

R.Julian R. Abel, Hantao Zhang
1998 Discrete Mathematics  
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.  ...  Vincent University when part of this resarch was done and wishes to thank their Department of Mathematics for the services provided.  ... 
doi:10.1016/s0012-365x(97)00021-6 fatcat:ntkvmnkfz5balnz7z6eazeop5a