New results on orthogonal arrays OA(3,5,4n + 2)

An orthogonal array of index unity, order v, degree 5 and strength 3, or an OA$(3,5,v)$ in short, is a $5\times v^3$ array on v symbols and in every $3\times v^3$ subarray, each 3-tuple column vector occurs exactly once. The existence of an OA$(3,5,4n+2)$ is still open except for few known infinite classes of n. In this paper, we introduce a new combinatorial structure called three dimensions orthogonal complete large sets of disjoint incomplete Latin squares and use it to obtain many new infinite classes of OA$(3,5,4n+2)$s.