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Dec 23, 2016 at 10:54 comment added Janne Kokkala To add (I'll include this in the answer later if I have more to edit) if you're not familiar with Latin squares: For prime power $k$, you can generate $k-1$ MOLS of order $k$ here and take the first $6$ rows of first $6$ squares to get the rectangles. For $k=10$ I don't know the construction off the top of my head.
Dec 23, 2016 at 10:03 history answered Janne Kokkala CC BY-SA 3.0