On the Existence of Four MOLS with Equal-sized Holes
by
Frank E. Bennett
Mount Saint Vincent University
Coauthors: Gennian Ge (Suzhou University), Julian Abel (University of New South Wales)

In this paper, we investigate the existence of four MOLS (mutually orthogonal Latin squares) having holes, corresponding to missing sub-MOLS, which are disjoint and spanning. We show that four MOLS with n holes of size h exist for most cases where h >= 2 and n >= 6. In particular, our results provide substantial improvements to those reported in Table 3.21 of "The CRC Handbook of Combinatorial Designs", (C. J. Colbourn and J. H. Dinitz, eds.), CRC Press Inc., 1996, pp.170-171.

Date received: October 3, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafn-14.