An infinite class of 2-designs with containing a -invariant oval

For each q = 2 m , m ≥ 1 , an infinite class of 2- ( q 4 + q + 1 , q + 1 , 1 ) designs admitting P S U ( 3 , q ) as an automorphism group is constructed. Such designs are shown to contain embedded Desarguesian projective planes of order q and a P S U ( 3 , q ) -invariant oval.