Elliptic semiplanes and group divisible designs with orthogonal resolutions

In this paper we prove that there exists an elliptic semiplaneS(v, k, m) withk –m 2 if and only if there exists a group divisible design GDD_k((k –m)(k – 1);k –m; 0, 1) withm pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplaneW(45, 7, 3) and show thatW is isomorphic to the elliptic semiplaneS(45, 7, 3) given by R. D. Baker.