Completing the spectrum of semiframes with block size three

A $k$-semiframe of type $g^u$ is a $k$-GDD of type $g^u\left(X,G,ℬ\right)$, in which the collection of blocks $ℬ$ can be written as a disjoint union $ℬ=P\cup Q$, where $P$ is partitioned into parallel classes of $X$ and $Q$ is partitioned into holey parallel classes, each holey parallel class being a partition of $X\backslash G$ for some $G\in G$. In this paper, we will introduce a new concept of $t$-perfect semiframe and use it to prove the existence of a 3-semiframe of type $g^u$ with even group size. This completes the proof of the existence of 3-semiframes with uniform group size.