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Disjoint blocks in a \(\mathrm{MOL}(6)\). (English) Zbl 1466.05018

Summary: We prove that the maximal number of pairwise disjoint 4-blocks in a \(\mathrm{MOL}(6)\) is 3. We recall various proofs for the non-existence of a \(\mathrm{MOL}(6)\) and show: with the theorem the proofs can be simplified considerably.

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares
05B30 Other designs, configurations
05A15 Exact enumeration problems, generating functions
05D15 Transversal (matching) theory
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