On Exact Bicoverings of \(12\) Points

J.L. Allston1, M.J. Grannell2, T.S. Griggs2, K.A.S. Quinn2, R.G. Stanton3
1National Research Council of Canada 435 Ellice Avenue, Winnipeg Manitoba, R3B 1Y6 Canada
2Department of Pure Mathematics The Open University Walton Hall, Milton Keynes, MKT GAA United Kingdom
3Department of Computer Science University of Manitoba Winnipeg, Manitoba, R3T 2N2 Canada

Abstract

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 \(g(2, 2; 12) \geq 14\).