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，若将它们叠加后恰好有$r$个不同的有序对。对于$n$阶拉丁方，所有可能的$r$值谱系已知。若$n$阶拉丁方$A$与其转置矩阵构成$r$-正交对，则称$A$为$r$-自正交的。除$n=14$外，所有阶数$n$对应的$r$值谱系均已明确。我们开发了用于计算$n$阶$r$-正交拉丁方对的随机算法，以及计算$n$阶$r$-自正交拉丁方的算法。