Nested BIBDs from affine planes

For any prime power q, there exists an affine plane of order q. The complement of an affine plane is a balanced incomplete block design (131131)) with block size q(2) - q. In this note, a proof is given that the blocks can be split into sub-blocks to form a nested BIBD with parameters (q(2), q(2) +q,q(3) +q(2), q(2) - 1, q(2) -q,q - 1). Alternatively, this is a generalized tournament design with one game each round, involving q teams, each team with q - 1 players.