Super-simple BIBDs with block size 4 and index 7
type: Item
instance of: scholarly article
title: Super-simple BIBDs with block size 4 and index 7
zbMATH Open document ID: 1448.05022
author: Xianwei Sun
published in: Discrete Mathematics
publication date: 2020-10-08T00:00:00Z
review text: A design is called simple if it contains no repeated blocks. A design is said to be super-simple if the intersection of any two blocks has at most two elements. The main result of this paper, deduced by direct and recursive constructions is the following: The necessary conditions for existence of a super-simple \((v,4,7)\)-BIBD, namely \(v\equiv 1, 4\) (mod 12) and \(v\geq 16\), are also sufficient. Note that the existence of super-simple \((v,4,\lambda)\)-BIBDs has been previously determined for \(\lambda=2,3,4,5,6\) and \(9\) and when \(\lambda =7\), only the necessary conditions were known.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 7257923
zbMATH Keywords: BIBD
zbMATH Keywords: super-simple design
zbMATH Keywords: group divisible design
zbMATH Keywords: recursive construction
reviewed by: Ioan Tomescu
MaRDI profile type: Publication
full work available at URL: j.disc.2020.112089
OpenAlex ID: W3080196175
cites work: Super-simple Steiner pentagon systems
cites work: Q4337362
cites work: New upper bounds on the minimum size of covering designs
cites work: Super-simple designs with \(v\leq 32\)
cites work: Super-simple balanced incomplete block designs with block size 4 and index 5
cites work: Q4697578
cites work: On the existence of super-simple \((v,4,4)\)-BIBDs
cites work: Uniformly resolvable decompositions of \(K_v\) into \(K_2\) and \(K_{1, 3}\) graphs
cites work: Super-simple balanced incomplete block designs with block size 4 and index 6
cites work: Super-simple balanced incomplete block designs with block size 5 and index 3
cites work: Super-simple \((\nu, 5, 5)\) designs
cites work: Super-simple \((v,5,4)\) designs
cites work: Q3411976
cites work: Q4888375
cites work: Super-simple (\(v\),\,5,\,2)-designs.
cites work: Q4016822
cites work: Q4508621
cites work: Q4304329
cites work: On optimal superimposed codes
cites work: A combinatorial construction for perfect threshold schemes
cites work: Decomposable super‐simple RBIBDs with block size 4 and index 6
cites work: Decomposable super‐simple NRBIBDs with block size 4 and index 6
cites work: Super-simple balanced incomplete block designs with block size 4 and index 9
DOI: 10.1016/J.DISC.2020.112089
description: scientific article; zbMATH DE number 7257923