Improvements for lower bounds of mutually orthogonal Latin squares of sizes $54$, $96$ and $108$

R. Julian R. Abel, Ingo Janiszczak, Reiner Staszewski

We will show that there are at least 8, 10 and 9 mutually orthogonal Latin squares (MOLS) of orders $n=54$, $96$ and $108$. The cases $n=54$ and $96$ are obtained by constructing s…