Appendage to: Multi-part balanced incomplete-block designs

  • R. A. BaileyEmail author
  • Peter J. Cameron
Open Access
Short Communication

1 Appendage to: Statistical Papers

Soon after the publication of Bailey and Cameron (2019), we became aware of the paper by Martin (1998). This paper uses the name ‘mixed block designs’ for the special case of our designs with exactly two parts, but slightly generalized to allow \(\lambda _{ii}=0\) for either \(i=1\) or \(i=2\). It was contemporaneous with Mukerjee (1998), but independent of that and of Sitter (1993). Furthermore, relaxing the conditions that \(k_1\) and \(k_2\) are both constant across blocks to the condition that the total \(k_1+k_2\) is constant across blocks gives the ‘balanced bipartite block designs’ introduced by Kageyama and Sinha (1988) and Sinha and Kageyama (1990).

The first four constructions in Bailey and Cameron (2019, Sect. 2) are given in Martin (1998, Sect. 1). The lower bound in our Eq. (4) is given in Theorem 2.2 of Martin (1998).



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© The Author(s) 2019

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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsUK
  2. 2.School of Mathematical SciencesQueen Mary University of LondonLondonUK

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