On the indecomposable partition problem: IPP(10,Λ)

In this paper, we determine all indecomposable triple systems of order 10 and index 4 with a non-trivial automorphism group and show that exactly 101 such designs exist. We then answer some questions about IPP(10,Λ) and finally obtain a lower bound for the number of LS[4](2,3,10).