General direct construction methods were published by Morgan & Uddin, Greig & Rees and others.
The methods of construction were given in Greig and Rees.
This paper gave general results, and nearly all the designs for k=3, while Abel, Greig & Rees gave the remaining solutions for k=3 and nearly all the solutions for k=4. (The latter also included general results for Nested OBIBDs and nearly all the solutions for k1=4, k2=2.)
The solutions for k=3 have been collected into an applet (see menu above), and I hope to do another for k=4 before long.