In this investigation we derive a few properties of the intersection of blocks in a balanced incomplete block (b.i.b. for conciseness) design with parameters $v, b, r, k, \lambda$ and discuss the divisibility of $v$ by $k$. The last section deals with certain characteristic properties of symmetric and affine resolvable b.i.b. designs.
"On the Parameters and Intersection of Blocks of Balanced Incomplete Block Designs." Ann. Math. Statist. 33 (3) 1200 - 1205, September, 1962. https://doi.org/10.1214/aoms/1177704485