Unitals in the Hölz design on 28 points
type: Item
instance of: scholarly article
title: Unitals in the Hölz design on 28 points
zbMATH Open document ID: 0731.05010
DOI: 10.1007/BF00181198
author: Vladimir D. Tonchev
published in: Geometriae Dedicata
publication date: 1991-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 4208085
zbMATH Keywords: Hölz design
zbMATH Keywords: unital
reviewed by: William E. Cherowitzo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4208085