A block intersection number of a block design is a nonnegative integer 
for which the design has two
distinct blocks 
and 
satisfying
 |
Thus the block intersection numbers record the possible sizes of intersections between distinct blocks. Their multiplicities, which count the pairs of blocks having each intersection size, can distinguish nonisomorphic block designs with the same parameters (Kaspers and Pott 2020).
For example, every two distinct lines of a projective plane meet in one point, so a projective plane viewed as a block design has the single block intersection number 1. More generally, a symmetric block design has a single block intersection number.
