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

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 \( 5 \).