Efficient semi-Latin rectangles: designs for plant disease experiments

Experiments on disease in plants often use half-leaves as experimental units. The whole leaves are typically in the rectangular array formed by h leaf-heights (rows) and p plants (columns), where h < p. We specialize to the case where h=n and p=2n and there are 2n treatments. If each treatment occurs once per column and twice per row, we call such a design a semi-Latin rectangle. Efficient semi-Latin rectangles of such sizes are constructed for 2 \leq n \leq 10. Guidance is given on their use.