Construction of strongly regular graphs using affine designs

Suppose there exist a balanced incomplete block design with λ = 1 and an affine resolvable balanced incomplete block design, the two designs having the same replication number. Combining these designs we construct two strongly regular graphs. This is applied to give a new family of design graphs (( v , k , λ)-graphs). Finally, we show that for any prime power n there are two non-isomorphic design graphs with v = n 2 ( n +2), k = n ( n +1) and λ = n .