Unitals in the Hölz-design on 28 points

In this paper, we provide a theoretical proof of the fact that the only unitals contained in the 2-(28,4,5) Hölz design are Hermitian and Ree unitals (as was previously proven by a computer search by Tonchev, [V.D. Tonchev, Unitals in the Hölz design on 28 points, Geom. Dedicata 38 (3) (1991) 357–363]).