On an infinite class of Steiner systems constructed from affine spaces
type: Item
instance of: scholarly article
title: On an infinite class of Steiner systems constructed from affine spaces
zbMATH Open document ID: 0584.05012
DOI: 10.1007/BF01191366
author: Ascher Wagner
author: J. D. Key
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: The authors show that a construction introduced by \textit{E. F. Assmus} and \textit{J. D. Key} [On an infinite class of Steiner systems with \(t=3\) and \(k=6\), J. Comb. Theory, Ser. A 42 (1986)] can be adapted to apply to the designs of points and lines of the finite affine spaces AG(d,q) for \(q\geq 3\). An infinite class of \(3-(q^ d+1,q+1,1)\) designs is constructed for \(d>2\), \(q\geq 3\), by extending the 2-design of points and lines of AG(d,q) in the following way: a new point ''\(\infty ''\) is adjoined to each line in AG(d,q), and for each plane AG(2,q) in AG(d,q), an arbitrary class of ovals in the plane is chosen so that the plane is extended to an inversive plane. In this way, new 3-designs are constructed that are shown not to be isomorphic to the Witt designs [see, for example, \textit{D. R. Hughes} and \textit{F. C. Piper}, Design Theory (1985; Zbl 0561.05009)]. The authors also note that the class of designs constructed is not the same as that constructed by \textit{H. Hanani} [J. Comb. Theory, Ser. A 26, 1-19 (1979; Zbl 0395.05007)] of the same parameters, although there is some overlap.
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 3935051
zbMATH Keywords: Steiner systems
zbMATH Keywords: 3-designs
zbMATH Keywords: Witt designs
MaRDI profile type: Publication
Recommended article: On infinite Steiner systems
Recommended article: Defining sets for the Steiner triple systems from affine spaces
Recommended article: Q3762328
Recommended article: A Construction of Almost Steiner Systems
Recommended article: Q4386079
Recommended article: Note on large sets of infinite steiner systems
Recommended article: The sets of type (0,n) and the Steiner triple systems in a finite affine plane
Recommended article: Some inequalities for Steiner systems
Recommended article: Some remarks on Steiner systems
description: scientific article; zbMATH DE number 3935051