Steiner triple systems intersecting in pairwise disjoint blocks (Q1883637)

Summary: Two Steiner triple systems \((X,{\mathcal A})\) and \((X,{\mathcal B})\) are said to intersect in \(m\) pairwise disjoint blocks if \(|{\mathcal A} \cap{\mathcal B} |=m\) and all blocks in \({\mathcal A}\cap{\mathcal B}\) are pairwise disjoint. For each \(v\), we completely determine the possible values of \(m\) such that there exist two Steiner triple systems of order \(v\) intersecting in \(m\) pairwise disjoint blocks.