  In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic
triple systems for all v congruent to 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4
or v>11, using Skolem-type sequences. We construct, using Skolem-type
sequences, three-fold triple systems having the properties of being cyclic,
simple, and indecomposable for all admissible orders v, with some possible
exceptions for v = 9 and v = 24c + 57, where c >1 is a constant. To prove the
simplicity we used a Mathematica computer program. We list in the Appendix the
code and the results of the program.
