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Generalized Bhaskar Rao designs with block size 4 signed over elementary abelian groups. (English) Zbl 1037.05007

In a paper published in 1984, W. de Launey and J. Seberry [Combinatorics and applications, Proc. Semin. in Honour of S. S. Shrikhande, Indian Statist. Inst., Calcutta/India 1982, 311–316 (1984; Zbl 0702.05019)] investigated the existence of generalized Bhaskar Rao designs with block size 4 signed over elementary abelian groups and showed that the necessary conditions for the existence of a \((v,4,\lambda; \text{EA}(g))\) GBRD are sufficient for \(\lambda >g\) with 70 possible exceptions. In this paper, the authors use more recent work such as current lists of PBDs, new computational results, and connections to other designs to extend the 1984 paper. They reduce the possible exceptions to just a \((9,4,18h; \text{EA}(9h))\) GBRD, where the \(\gcd(6,h)=1\), and show that for \(\lambda=g\) the necessary conditions are sufficient for \(v> 46\). The appendix of the paper contains a list of corrections to the 1984 paper by de Launey and Seberry.

MSC:

05B05 Combinatorial aspects of block designs

Citations:

Zbl 0702.05019