Indecomposable Simple \(2-(v,\&, 4)\) Designs of Small Orders

In this paper, simple \(2-(9,4,\lambda)\) designs are constructed for \(\lambda = 3q\), \(1 \leq q \leq 7\), and indecomposable simple \(2-(v,k,\lambda)\) designs are constructed for all \(10 \leq v \leq 16\) and the smallest possible \(\lambda\) for which the existence of simple \(2-(v,k,\lambda)\) designs was previously undecided.