On $\lambda$-fold coverings with maximum block size four for $\lambda = 3, 4$ and 5

Grannell, Mike; Griggs, Terry and Stanton, R. G. (2004). On $\lambda$-fold coverings with maximum block size four for $\lambda = 3, 4$ and 5. Journal of Combinatorial Mathematics and Combinatorial Computing, 51, pp. 137–158.

Abstract

The minimum number of blocks having maximum size precisely four that are required to cover, exactly $\lambda$ times, all pairs of elements from a set of cardinality $v$ is denoted by $g_{\lambda}^{(4)}(v)$. We present a complete solution to this problem for $\lambda=3,4$ and 5.

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