| Summary: | A compatible factorization of order v, is a v × (v−1)2 array of distinct triples in which row i form a near-one-factor with focus i. This article aims to develop compatible factorization to display v×( v−1 2 −2 3 ) triples with minimum repetition. Through this article, we propose and define a new type of factorization called near-compatible factorization. First, we prove the existence of near-compatible factorization. Then, the construction will be presented based on difference triple method. Finally, we employ this near-compatible factorization to illustrate the development of triple design, that is called near-triad design
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