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Nested Optimal λ-Packings and λ-Coverings of Pairs with Triples

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Abstract

We say that an optimal λ-packing ( λ-covering) of pairs with triples can be nested if it is possible to add one point to each block such that an optimal 2 λ-packing (2 λ-covering) of pairs with quadruples is obtained. A packing (covering) of order v can exist only if v ≥ 4 and v / 3 λ(v - 1) / 2 = v / 4 2λ(v - 1) / 3 ( v / 3 λ(v - 1) / 2 = v / 4 2λ (v - 1) / 3 ). It is shown in this paper that this condition is also sufficient, except possibly for v = 20.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada, A1C 557

    Nabil Shalaby

  2. Department of Mathematics, Suzhou University, Suzhou, 215006, P. R. China

    Jianxing Yin

Authors
  1. Nabil Shalaby
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  2. Jianxing Yin
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Shalaby, N., Yin, J. Nested Optimal λ-Packings and λ-Coverings of Pairs with Triples. Designs, Codes and Cryptography 15, 271–278 (1998). https://doi.org/10.1023/A:1008373226759

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  • DOI: https://doi.org/10.1023/A:1008373226759

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