Cyclic, Simple and Indecomposable Three-Fold Triple Systems

In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triplesystems for all v ≡ 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4 or v ≥ 12, using Skolem-type sequences.We construct, using Skolem-type sequences, three-fold triple systems having theproperties of being cyclic, simple, and indecomposable for all admissible orders v, withsome possible exceptions for v = 9 and v = 24c + 57, where c ≥ 2 is a constant.To prove the simplicity we used a Mathematica computer program. We list in theAppendix the code and the results of the program.