On exact bicoverings of 12 points

Allston, J. L.; Grannell, M. J.; Griggs, T. S.; Quinn, K. A. S. and Stanton, R. G. (2000). On exact bicoverings of 12 points. Ars Combinatoria, 55 pp. 147–159.

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 $13\le g(2,2;12)\le 16$. We prove that $g(2,2;12)\ge 14$.

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