On the existence of partitionable skew Room frames

Partitionable skew Room frames of type hn have played an important role in the constructions of 4-frames, (K4 − e)-frames and super-simple (4, 2)-frames. In this paper, we investigate the existence of partitionable skew Room frames of type hn. The necessary conditions for the existence of such a design are that h(n − 1) ≡ 0 (mod 4) and h 5. It is proved that these necessary conditions are also sufficient with a few possible exceptions. As a byproduct, the known results on the existence of skew Room frames and uniform 4-frames are both improved. © 2007 Elsevier B.V. All rights reserved. MSC: Primary, 05B15;