All directed BIBDs with k = 3 exist

A directed BIBD with parameters (v,b,r,k,λ*) is a BIBD with parameters (v, b, r, k, 2λ*) in which each ordered pair of varieties occurs together in exactly λ* blocks. It is shown that λ*v(v - 1) = 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (v, b, r, k, λ*) BIBD with k = 3.