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For $X, Y, Z \\subseteq \\{1, ... ,n\\}$, let $L(X, Y. Z)$ be the number of triples $i\\in X, j\\in Y, k\\in Z$ such that $L(i,j) = k$. We conjecture that asymptotically almost every Latin square satisfies $|L(X, Y, Z) - \\frac 1n |X||Y||Z||\\le O(\\sqrt{|X||Y||Z|})$ for every $X, Y$ and $Z$. Let $\\varepsilon(L):= \\max |X||Y||Z|$ when $L(X, Y, Z)=0$. The above conjecture implies that $\\varepsilon(L) \\le O(n^2)$ holds asymptotically almost surely (this bound is obviously tight). 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