We investigate MacNeish's conjecture (known to be false in general) in the setting of what we call "transitive" Mutually Orthogonal Latin Squares (MOLS). When we restrict our attention to "simply transitive" MOLS, we find that the conjecture holds. We provide some partial results towards the transitive case, as well as the outcome of a computer search, which introduces a new construction of MOLS. In particular, we were unable to find any transitive large (conjecture-violating) sets of MOLS in the literature.

翻译：本文研究了在所谓"传递"互正交拉丁方（MOLS）背景下MacNeish猜想（已知该猜想在一般情况下不成立）的表现。当我们将注意力限制在"单传递"MOLS时，发现该猜想成立。我们针对传递情形给出部分研究结果，同时呈现计算机搜索的成果——该搜索提出了一种新的MOLS构造方法。值得注意的是，我们在现有文献中未能发现任何违反猜想的传递性大规模MOLS集合。