Bhaskar Rao designs with block size four
type: Item
instance of: scholarly article
title: Bhaskar Rao designs with block size four
zbMATH Open document ID: 1018.05009
DOI: 10.1016/S0012-365X(03)00031-1
published in: Discrete Mathematics
publication date: 2003-07-29T00:00:00Z
review text: The \(v \times b\) incidence matrix of a balanced incomplete block design BIBD\((v,k,\lambda)\) has the property that the inner product of any two distinct rows is \(\lambda\). If the 1s of such an incidence matrix can be replaced by elements from \(\{-1,1\}\) so that the inner product of any two distinct rows is \(c\), then we say that we have a \(c\)-Bhaskar Rao design or a \(c\)-BRD\((v,k,\lambda)\). The current paper is the last one in a series of papers settling the existence problem for \(c\)-BRD\((v,4,\lambda)\). It resolves the 28 instances that were still open after recent progress by \textit{M. Greig, S. P. Hurd, J. S. McCranie} and \textit{D. G. Sarvate} [J. Comb. Des. 10, 361-386 (2002; Zbl 1012.05022)] and \textit{D. Deng, M. Greig} and \textit{P. R. J. Östergård} [Discrete Math. 261, 189-208 (2003; Zbl 1015.05012)]. A central observation in the paper is the equivalence between Bhaskar Rao designs and certain group divisible designs (GDDs).
reviewed by: Patric R. J. Östergård
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 1956046
zbMATH Keywords: Bhaskar Rao design
zbMATH Keywords: BIBD
zbMATH Keywords: group divisible design
author: Gennian Ge
author: Clement Lam
MaRDI profile type: Publication
cites work: Q4718791
cites work: Q5629087
cites work: ON THE CONSTRUCTION OF BALANCED INCOMPLETE BLOCK DESIGNS
cites work: On the \((v,5,\lambda)\)-family of Bhaskar Rao designs
cites work: Q4876941
cites work: Q3222213
cites work: Q3480050
cites work: More \(c\)-Bhaskar Rao designs with small block size
cites work: On group-divisible designs with block size four and group-type \(6^{u} m^{1}\).
cites work: On c‐Bhaskar Rao designs with block size 4
cites work: Q3996153
cites work: Generalized Bhaskar Rao designs
cites work: Q3832580
cites work: Regular group divisible designs and Bhaskar Rao designs with block size three
cites work: Generalized Bhaskar Rao designs of block size three
cites work: Q3901532
cites work: An existence theory for pairwise balanced designs. I: Composition theorems and morphisms
cites work: Generalized Steiner systems \(\text{GS}_4(2,4,v,g)\) for \(g=2,3,6\)
cites work: Some combinatorial constructions for optical orthogonal codes
full work available at URL: s0012-365x(03)00031-1
OpenAlex ID: W1982895103
description: scientific article; zbMATH DE number 1956046