More on exact bicoverings of 12 points

Grannell, M. J.; Griggs, T. S.; Maenhaut, B. M.; Quinn, K. A. S. and Stanton, R. G. (2003). More on exact bicoverings of 12 points. Ars Combinatoria, 69 pp. 197–213.

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 $v=3,4,\dots,11$ . It was previously known that $14\leq g(2,2;12)\leq16$ . We prove that $g(2,2;12) \geq 15$ .