Indecomposable large sets of Steiner triple systems with indices 5, 6

A family (X, B 1), (X, B 2), ., (X, B q ) of q STS(.)s is a .-fold large set of STS(.) and denoted by LSTS . (.) if every 3-subset of X is contained in exactly . STS(.)s of the collection. It is indecomposable and denoted by IDLSTS . (.) if there does not exist an LSTS..(.) contained in the collection for any .. < .. In this paper, we show that for . = 5, 6, there is an IDLSTS . (.) for . . 1 or 3 (mod 6) with the exception IDLSTS6(7).