Unitals in the Hölz design on 28 points
The Hölz design of order 3 is a 2-(28,4,5) design constructed from the point set of a Hermitian unital in PG(2,9) by adding new blocks (the intersections of the unital with certain Baer subplanes) to the blocks of th unital. Besides containing the initial Hermitian unital, the design also contains unitals of Ree type as subdesigns. In this paper it is shown that any unital (a 2-(28,4,1) design in the present situation) which occurs as a subdesign must be of either the Hermitian or Ree type. The author proceeds by counting all the unitals of the given types and then verifying by computer that no additional unitals exist.
scientific article; zbMATH DE number 4208085