On the existence of balanced incomplete block designs with nested rows and columns

In this paper we will give a construction of BIBRCs by utilizing the method of differences. Moreover, in the case when λ satisfies some conditions, we will prove that there exists a BIBRC(q,k1,k2,λ) if q is a sufficiently large prime power and λ(q-1)≡0(modk1k2(k1-1)(k2-1)) holds.