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).
References
Bailey RA, Cameron PJ (2019) Stat Pap 60:55–76
Kageyama S, Sinha K (1988) Some constructions of balanced bipartite block designs. Util Math 33:137–162
Martin WJ (1998) Mixed block designs. J Comb Des 6:151–163
Mukerjee R (1998) On balanced orthogonal multi-arrays: existence, construction and application to design of experiments. J Stat Plan Inference 73:149–162
Sinha K, Kageyama S (1990) Further constructions of balanced bipartite block designs. Util Math 38:155–160
Sitter RR (1993) Balanced repeated replications based on orthogonal multi-arrays. Biometrika 80:211–221
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Bailey, R.A., Cameron, P.J. Appendage to: Multi-part balanced incomplete-block designs. Stat Papers 62, 1557–1558 (2021). https://doi.org/10.1007/s00362-019-01137-4
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DOI: https://doi.org/10.1007/s00362-019-01137-4