论文标题
成对的摩尔摩尔十个满足非平凡关系的摩尔
Pairs of MOLS of order ten satisfying non-trivial relations
论文作者
论文摘要
$ k $ -net $（n）$的关系（或等效地，一组$ k-2 $互惠正交拉丁正方形的订单$ n $）是$ \ mathbb {f} _ {2} $线性依赖在网的发生率矩阵中。 Dukes and Howard（2014）表明，任何6（10）至少满足两个非平凡关系，并将可能出现在这样的网络中出现的关系分类。我们发现，直到等价，有1826 \，320 $的摩尔对满足至少一个非平凡的关系。这些对都没有扩展到三倍。我们还排除了来自Dukes和Howard的分类的一组$ 3 $ -MOL的其他关系。
A relation on a $k$-net$(n)$ (or, equivalently, a set of $k-2$ mutually orthogonal Latin squares of order $n$) is an $\mathbb{F}_{2}$ linear dependence within the incidence matrix of the net. Dukes and Howard (2014) showed that any 6-net(10) satisfies at least two non-trivial relations, and classified the relations that could appear in such a net. We find that, up to equivalence, there are $18\,526\,320$ pairs of MOLS satisfying at least one non-trivial relation. None of these pairs extend to a triple. We also rule out one other relation on a set of $3$-MOLS from Dukes and Howard's classification.
