On $\lambda$-fold Coverings with Maximum Block Size Four for $\lambda =3,4$ and $5$

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 $v=3,4,$ and $5$.