New \(t\)-designs and large sets of \(t\)-designs
type: Item
instance of: scholarly article
title: New \(t\)-designs and large sets of \(t\)-designs
zbMATH Open document ID: 0936.05010
DOI: 10.1016/S0012-365X(99)90047-X
author: Anton Betten
author: Alfred Wassermann
author: Reinhard Laue
published in: Discrete Mathematics
publication date: 1999-01-01T00:00:00Z
review text: The authors report the results of their computer-aided search for simple \(t\)-\((v,k,\lambda)\) designs and large sets of designs. The main tool used in their search is the computer program DISCRETA developed by the authors and based on the method of Kramer and Mesner [see \textit{E. S. Kramer} and \textit{D. M. Mesner}, Discrete Math. 15, 263-296 (1976; Zbl 0362.05049)] further combined with some previously known recursive methods. The paper provides a brief list of the recursive methods used and a short description of the use of DISCRETA (which allows one to choose the automorphism group for the prospective design, and appears to be rather user friendly). A table of all the presently known simple \(t\)-\((v,k,\lambda)\) designs, \(t\geq 7\) and \(v\leq 40\), is included (most of them found by the authors) as well as several results on the existence of infinite families of large sets of \(t\)-designs.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1322004
zbMATH Keywords: computer search
zbMATH Keywords: large sets of \(t\)-designs
reviewed by: Robert Jajcay
describes a project that uses: ATLAS Group Representations
describes a project that uses: DISCRETA
MaRDI profile type: Publication
cites work: Extending large sets of \(t\)-designs
cites work: Extending t-designs
cites work: Q4352791
cites work: Simple \(8\)-designs with small parameters
cites work: Q4357339
cites work: Q4393344
cites work: Q4237669
cites work: Simple 8-(40, 11, 1440) designs
cites work: Q4877001
cites work: Combining \(t\)-designs
cites work: Allgemeine Schnittzahlen in t-Designs. (General intersection numbers in t-designs)
cites work: Q3710534
cites work: t-designs on hypergraphs
cites work: Q4876923
cites work: The existence of simple \(6\text{-}(14,7,4)\) designs
cites work: Factoring polynomials with rational coefficients
cites work: Q3340868
cites work: Q5626681
cites work: On t-designs
cites work: Q4254898
cites work: The t‐designs with prescribed automorphism group, new simple 6‐designs
cites work: Q4266548
cites work: Q2757225
cites work: Non-trivial \(t\)-designs without repeated blocks exist for all \(t\)
cites work: Locally trivial t-designs and t-designs without repeated blocks
cites work: On the construction of \(t\)-designs and the existence of some new infinite families of simple 5-designs
cites work: High order intersection numbers of \(t\)-designs
cites work: Q4222123
full work available at URL: s0012-365x(99)90047-x
OpenAlex ID: W4213006630
description: scientific article; zbMATH DE number 1322004