Two Latin squares of order $n$ are $r$-orthogonal if, when superimposed, there are exactly $r$ distinct ordered pairs. The spectrum of all values of $r$ for Latin squares of order $n$ is known. A Latin square $A$ of order $n$ is $r$-self-orthogonal if $A$ and its transpose are $r$-orthogonal. The spectrum of all values of $r$ is known for all orders $n\ne 14$. We develop randomized algorithms for computing pairs of $r$-orthogonal Latin squares of order $n$ and algorithms for computing $r$-self-orthogonal Latin squares of order $n$.

翻译：两个 $n$ 阶拉丁方称为 $r$-正交的，如果它们叠加时恰好存在 $r$ 个不同的有序对。已知 $n$ 阶拉丁方的所有 $r$ 值的谱。如果 $n$ 阶拉丁方 $A$ 及其转置是 $r$-正交的，则称 $A$ 为 $r$-自正交的。对于所有 $n \ne 14$ 的阶数，已知所有 $r$ 值的谱。我们开发了用于计算 $n$ 阶 $r$-正交拉丁方对的随机算法，以及用于计算 $n$ 阶 $r$-自正交拉丁方的算法。