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A lower bound on HMOLS with equal sized holes
[article]
2020
arXiv
pre-print
It is known that N(n), the maximum number of mutually orthogonal latin squares of order n, satisfies the lower bound N(n) ≥ n^1/14.8 for large n. For h≥ 2, relatively little is known about the quantity N(h^n), which denotes the maximum number of 'HMOLS' or mutually orthogonal latin squares having a common equipartition into n holes of a fixed size h. We generalize a difference matrix method that had been used previously for explicit constructions of HMOLS. An estimate of R.M. Wilson on higher
arXiv:2008.08788v1
fatcat:nq7ot5kqlrfovmlw5xilaa2uzm