We verify that \(6\) more of the tum squares of order \(10\) cannot be completed to a triple of mutually orthogonal Latin squares of order \(10\). We find a pair of orthogonal Latin squares of order \(10\) with \(6\) common transversals, \(5\) of which have only a single intersection, and a pair with \(7\) common transversals.
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