It is proved that a strongly balanced uniform repeated measurement design (R.M.D.) is D-optimum among all R.M.D. for the estimation of the treatment effects. The proof relies on the inequality \((B'A^+B)^{-1}\leq B^+AB^{\prime +}\).
If in a column-complete Latin square the rows represent the periods and the columns the experimental units, then a row-column design can be considered as an R.M.D. It is proved that a column-complete Latin square design of order t is D-optimum of all R.M.D. for the estimation of treatment effects.