We determine those triples \((g, u, k)\) for which there exists a pair of group divisible designs with block size \(3\), each on the same \(u\) groups of size \(g\), having exactly \(k\) blocks in common.
Citation
R.A.R. Butler, D.G. Hoffman. Intersections of Group Divisible Triple Systems[J], Ars Combinatoria, Volume 034. 268-288. .