A note on orthogonal Graeco-Latin designs

It is shown that Graeco-Latin block designs which have treatments totally balanced with respect to blocks in each set and which are pairwise orthogonal with respect to the other set can be constructed with parameters v1 = r2 = p + 1, r1 = v2 = p, b = 2p, k = (p+l)/2 for p a prime power. Moreoever they can be represented in a compact manner and previously ad hoc examples become part of the series.