Recursive constructions and some properties of twofold designs with block size four

Abstract A direct construction for partially resolvable t -partitions is presented and then used to give a recursive construction for BIBDs (ν, 4, 2). In particular, we construct BIBD(ν, 4, 2) with BIBD(ν, 4, 2) embedded in it whenever ν = 3 u + a, a ∈ {1, 4, 7}. This result allows us to give simple proofs for the existence of BIBD(ν, 4, 2) with various additioinal properties.