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Donovan, Diane; Grannell, Mike and Yazici, Emine Şule
(2020).
DOI: https://doi.org/10.1016/j.disc.2020.111835
Abstract
In this paper it is shown that any partial Latin square of order can be embedded in a Latin square of order at most
which has at least
mutually orthogonal mates. Further, for any
, it is shown that a pair of orthogonal partial Latin squares of order
can be embedded in a set of
mutually orthogonal Latin squares (MOLS) of order a polynomial with respect to
. A consequence of the constructions is that, if
denotes the size of the largest set of MOLS of order
, then
. In particular, it follows that
, improving the previously known lower bound
.