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Donovan, D. M. and Grannell, M. J.
(2013).
DOI: https://doi.org/10.1016/j.jcta.2013.05.004
URL: http://www.sciencedirect.com/science/article/pii/S...
Abstract
Bounds are obtained on the number of distinct transversal designs TD (having
groups with
points in each group) for certain values of
and
. Amongst other results it is proved that, if
where
is a prime power, then the number of nonisomorphic TD
designs is at least
as
, where
. The bounds obtained give equivalent bounds for the numbers of distinct and nonisomorphic sets of
mutually orthogonal Latin squares of order
in the corresponding cases. Applications to other combinatorial designs are also described.