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Appendage to: Multi-part balanced incomplete-block designs

  • R. A. BaileyEmail author
  • Peter J. Cameron
Open Access
Short Communication
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1 Appendage to: Statistical Papers  https://doi.org/10.1007/s00362-018-01071-x

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).

Notes

References

  1. Bailey RA, Cameron PJ (2019) Stat Pap 60:55–76CrossRefGoogle Scholar
  2. Kageyama S, Sinha K (1988) Some constructions of balanced bipartite block designs. Util Math 33:137–162MathSciNetzbMATHGoogle Scholar
  3. Martin WJ (1998) Mixed block designs. J Comb Des 6:151–163MathSciNetCrossRefGoogle Scholar
  4. Mukerjee R (1998) On balanced orthogonal multi-arrays: existence, construction and application to design of experiments. J Stat Plan Inference 73:149–162MathSciNetCrossRefGoogle Scholar
  5. Sinha K, Kageyama S (1990) Further constructions of balanced bipartite block designs. Util Math 38:155–160MathSciNetzbMATHGoogle Scholar
  6. Sitter RR (1993) Balanced repeated replications based on orthogonal multi-arrays. Biometrika 80:211–221MathSciNetCrossRefGoogle Scholar

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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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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