Bhaskar Rao designs with block size four
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).
scientific article; zbMATH DE number 1956046
scientific article