Existence of DBIBDs with block size not divided by four 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(v,k,λ) 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.