The intersection problem for \(\text{PBD}(5^{*},3)\)s (Q2468021)

The intersection problem in design theory asks for determining all pairs \((v,k)\) such that there exist designs \((S,B_1)\) and \((S,B_2)\) of the prescribed type and order \(v\) with the property \(| B_1 \cap B_2|=k\). In this paper the intersection problem is completely solved for pairwise balanced designs with exactly one block of size \(5\) and the other blocks of size \(3\).