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In this note we show that for each Latin square $L$ of order $n\geq 2$, thereexists a Latin square $L'\neq L$ of order $n$ such that $L$ and $L'$ differ inat most $8\sqrt{n}$ cells. Equivalently, each Latin square of order $n$contains a Latin trade of size at most $8\sqrt{n}$. We also show that the sizeof the smallest defining set in a Latin square is $\Omega(n^{3/2})$. %That is,there are constants $c$ and $n_0$ such that for any $n>n_0$ the size of thesmallest defining %set of order $n$ is at least $cn^{3/2}$.

On the distances between Latin squares and the smallest defining set size