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.

中文翻译：

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正交数组 OA(3,5,4n + 2) 的新结果

索引统一、阶数v 、度数 5 和强度 3的正交数组，或 OA$（3,5,v）$简而言之，是一个$5\times v^3$v符号上的数组以及每个$3\times v^3$子数组中，每个 3 元组列向量恰好出现一次。OA的存在$（3,5,4n+2）$除了少数已知的无限类n之外，仍然是开放的。在本文中，我们引入了一种新的组合结构，称为三维正交完全大集不相交不完全拉丁方，并用它来获得许多新的无限类OA$（3,5,4n+2）$s。