The existence of directed BIBDs Original Research Article

For any positive integers k⩾3 and λ, let cd(k,λ) denote the smallest integer such that the necessary conditions 2λ(v−1)≡0 (mod k−1) and λv(v−1)≡0 (mod (k2)) for the existence of a DB(k,λ;v) are also sufficient for every v⩾cd(k,λ). In this article we provide an estimate for cd(k,λ) when k≡0 (mod 4) and any λ. Combined with the results in (Discrete Math. 222 (2000) 27–40), we completely give an estimate of cd(k,λ) for any integers k⩾3 and λ.