More Frames with Block Size Four

We present a new construction to obtain frames with block size four using certain skew Room frames. The existence results of Rees and Stinson for frames with block size four are improved, especially nfor hole sizes divisible by \(6\). As a by-product of the skew Room
frames we construct, we are also able to show that a resolvable \((K_4 – e)\)-design with \(60t + 16\) points exists if \(t \geq 0\) and \(t \neq 8, 12\).