The fundamental construction for 3-designs
type: Item
instance of: scholarly article
title: The fundamental construction for 3-designs
zbMATH Open document ID: 0792.05022
DOI: 10.1016/0012-365X(92)00055-V
author: Alan Hartman
published in: Discrete Mathematics
publication date: 1994-03-01T00:00:00Z
review text: The purpose of this paper is to extend the fundamental construction for group divisible designs of Wilson to one suitable for use in the construction of 3-designs. An important part of this is the generalization of the concept of a group divisible design and this is discussed in some detail. The construction simplifies in some special cases to similar known constructions. The construction is used to present simplified proofs of known results, especially for Steiner quadruple systems, that is 3-designs with four points in every block, and to give recursive theorems both for the construction of Steiner quadruple systems and for the construction of more general 3-designs with multiple block sizes.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 500612
zbMATH Keywords: group divisible designs
zbMATH Keywords: 3-designs
zbMATH Keywords: Steiner quadruple systems
MaRDI profile type: Publication
cites work: Q3737429
cites work: Intersections and supports of quadruple systems
cites work: Subdesigns in Steiner quadruple systems
cites work: On Quadruple Systems
cites work: The Existence and Construction of Balanced Incomplete Block Designs
cites work: On Some Tactical Configurations
cites work: Q5661898
cites work: On balanced incomplete block designs with blocks having five elements
cites work: Balanced incomplete block designs and related designs
cites work: A class of three-designs
cites work: Q3901525
cites work: Quadruple systems containing \(AG(3,2)\)
cites work: A general recursive construction for quadruple systems
cites work: Covering triples by quadruples: an asymptotic solution
cites work: Q3712344
cites work: Q5184924
cites work: Steiner quadruple systems - a survey
cites work: Q4065553
cites work: Q5284089
cites work: Q5627526
cites work: Some new constructions of 4-tuple systems
cites work: Q3966151
cites work: A general construction for group-divisible designs
cites work: An existence theory for pairwise balanced designs. I: Composition theorems and morphisms
cites work: Q4071247
cites work: An existence theory for pairwise balanced designs. III: Proof of the existence conjectures
full work available at URL: 0012-365x(92)00055-v
OpenAlex ID: W2003249853
description: scientific article; zbMATH DE number 500612