A note on generalization of distinct representatives

Agrawal (1966 Ann. Math. Statist. 37, 525-528) explored the concept of systems of distinct representatives to show that the treatments in a binary equireplicated incomplete block design can be rearranged within blocks such that the treatments occur as close to equally often as possible in every row. In this note, examples are given to show that Agrawal's proof is incomplete and a complete proof is presented. It follows from our modified proof that the same result also holds for non-binary or unequireplicated block designs.