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The Existence of (ν,6, λ)-Perfect Mendelsohn Designs with λ > 1

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Abstract.

The basic necessary conditions for the existence of a (v, k, λ)-perfect Mendelsohn design (briefly (v, k, λ)-PMD) are v ≥ k and λ v(v − 1) ≡ 0 (mod k). These conditions are known to be sufficient in most cases, but certainly not in all. For k = 3, 4, 5, 7, very extensive investigations of (v, k, λ)-PMDs have resulted in some fairly conclusive results. However, for k = 6 the results have been far from conclusive, especially for the case of λ = 1, which was given some attention in papers by Miao and Zhu [34], and subsequently by Abel et al. [1]. Here we investigate the situation for k = 6 and λ > 1. We find that the necessary conditions, namely v ≥ 6 and λ v(v − 1)≡0 (mod 6) are sufficient except for the known impossible cases v = 6 and either λ = 2 or λ odd.

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Authors and Affiliations

  1. School of Mathematics, University of New South Wales, Sydney, 2052, NSW, Australia

    R. J. R. Abel

  2. Department of Mathematics, Mount Saint Vincent University, Halifax, Nova Scotia, B3M 2J6, Canada

    F. E. Bennett

Authors
  1. R. J. R. Abel
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  2. F. E. Bennett
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Correspondence to R. J. R. Abel.

Additional information

Communicated by J. D. Key.

Researcher F.E. Bennett supported by NSERC Grant OGP 0005320.

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Abel, R.J.R., Bennett, F.E. The Existence of (ν,6, λ)-Perfect Mendelsohn Designs with λ > 1. Des Codes Crypt 40, 211–224 (2006). https://doi.org/10.1007/s10623-006-0008-4

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  • DOI: https://doi.org/10.1007/s10623-006-0008-4

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