The existence question for the family of \(4-(15,5,\lambda)\) designs has long been answered for all values of \(\lambda\) except \(\lambda = 2\). Here, we resolve this last undecided case and prove that \(4-(15, 5, 2)\) designs are constructible.
Citation
Ziba Eslami, G.B. Khosrovshahi, M. Mohammad-Noori, B. Taypeh-Rezaie. Some New \(4\)-Designs[J], Ars Combinatoria, Volume 073. 225-229. .