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Thwarts in transversal designs

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Abstract

A subset of points in a transversal design is athwart if each block in the design has one of a small number of intersection sizes with the subset. Applications to the construction of mutually orthogonal latin squares are given. One particular case involves inequalities for the minimum number of distinct symbols appearing in an α×β subarray of an×n latin square. Using thwarts, new transversal designs are determined for orders 408, 560, 600, 792, 856, 1046, 1059, 1368, 2164, 2328, 2424, 3288, 3448, 3960, 3992, 3994, 4025, 4056, 4824, 5496, 6264, 7768, 7800, 8096, and 9336.

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References

  1. R. J. R. Abel, private communications (1993).

  2. T. Beth, D. Jungnickel, and H. Lenz,Design Theory, Cambridge University Press, Cambridge (1986).

    Google Scholar 

  3. A. E. Brouwer, The number of mutually orthogonal latin squares, ZW 123, Math. Centre Amsterdam (1979).

  4. A. E. Brouwer and G. H. J. van Rees, More mutually orthogonal latin squares,Discrete Math., Vol. 39 (1982) pp. 263–281.

    Google Scholar 

  5. M. Wojtas, A note on mutually orthogonal latin squares, Komunikat nr. 236, Instytut Matematyki Politechniki Wroclawskiej (1978).

  6. R. M. Wilson, Concerning the number of mutually orthogonal latin squares.Discrete Math., Vol. 9 (1974) pp. 181–198.

    Google Scholar 

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Authors and Affiliations

  1. Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Charles J. Colbourn

  2. Mathematics, University of Vermont, 05405, Burlington, Vermont, USA

    Jeffrey H. Dinitz

  3. Institute of Mathematics, Technical University of Wroclaw, Wroclaw, Poland

    Mieczyslaw Wojtas

Authors
  1. Charles J. Colbourn
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  2. Jeffrey H. Dinitz
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  3. Mieczyslaw Wojtas
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Colbourn, C.J., Dinitz, J.H. & Wojtas, M. Thwarts in transversal designs. Des Codes Crypt 5, 189–197 (1995). https://doi.org/10.1007/BF01388383

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  • DOI: https://doi.org/10.1007/BF01388383

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