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