An enumeration on the structure of nonrepeated triples in a three-fold triple system

The normally used method to construct three-fold triple system is idempotent latin squares. This existing method only produces three-fold triple system that has repeated triples. Thus, this paper attempts to propose a method for developing three-fold triple system that can generate nonrepeated triples in the design. We employ compatible factorization design to formulate the method for distinct three-fold triple system. In this method we need to ascertain a starter set as a first set to begin with. Further, we make use of this starter set to produce the design of distinct three-fold triple system. As special reference, we are keen to exemplify for case v = 9.