λ-fold indecomposable large sets of Steiner triple systems

A family (X, B1), (X, B2), …, (X, Bq) of q STS(ν)s is a λ-fold large set of STS(v) and denoted by LSTSλ(ν) if every 3-subset of X is contained in exactly λ STS(ν)s of the collection. It is indecomposable and denoted by IDLSTSλ(ν) if there exists no LSTSλ′ (ν) contained in the collection for any λ′ 1 and orders ν ≡ 1,3 (mod 6) do there exist IDLSTSλ(ν)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(ν) (HLSTSλ(ν)) as auxiliary designs to establish a recursive construction for IDLSTSλ(ν) and show that there exists an IDLSTSλ(ν) for λ = 2, 3,4 and ν ≡ 1,3 (mod 6).