Throughout this section, I have adopted the notation (k2,k1)NBIBD(v) as a shorthand for NBIBD(v,v(v-1)/k1,v(v-1)/k2,v-1, k1,k2,k1-1,k2-1), and likewise for the incomplete designs.
General direct construction methods have been published by Jimbo & Kuriki, Abel et al and others.
If a PMD(v,k1,1) exists, and k2 is a factor of k1, then a (k2,k1)NBIBD(v) exists - see here.
The methods of construction given for Pitch Designs, Generalised Whist Designs, etc are not entirely suitable for plain NBIBDs, since they insist on resolvability. Likewise, the theorems of for the more general or the Federer types of NBIBD, are not entirely suitable either. For the most part, the theorems as given by Greig & Rees can be adapted: these are translated here.
Whist Designs exist for all v ≥ 4 of the form 4n or 4n+1. Generalised Whist Designs with 3 teams of 2 exist for all except possibly 5 cases, and for all except possibly 73 cases with 2 teams of 3 (seehere). NBIBDs exist for all of the former (see here), and see here for an attempt on the latter.