The minimum number of incomplete blocks required to cover, exactly \(\lambda\) times, all \(t\)-element subsets from a set \(V\) of cardinality \(v\) (\(v > t\)) is denoted by \(g(\lambda, t; v)\). The value of \(g(2, 2; v)\) is known for \(v = 3, 4, \ldots, 11\). It was previously known that \(13 \leq g(2, 2; 12) \leq 16\). We prove that \(g(2, 2; 12) \geq 14\).
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