Designs, Codes and Cryptography

, Volume 10, Issue 2, pp 203–222 | Cite as

Pairwise Balanced Designs with Consecutive Block Sizes

  • Alan C. H. Ling
  • Xiaojun Zhu
  • Charles J. Colbourn
  • Ronald C. Mullin


This paper deals with existence for pairwise balanced designs with block sizes 5,6 and 7, block sizes 6,7 and 8 and block sizes 7,8 and 9 and some consequences of these results.

Combinatorial designs PBD-closure finite linear spaces 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. J. R. Abel, Some new BIBDS with λ = 1 and 6 ≤ k ≤ 10, J. Combinatorial Designs, Vol. 4 (1996) pp. 27–50.Google Scholar
  2. 2.
    R. J. R. Abel, A. E. Brouwer, C. J. Colbourn and J. H. Dinitz, Mutually orthogonal latin squares (MOLS), CRC Handbook of Combinatorial Designs (C. J. Colbourn and J. H. Dinitz, eds.), CRC (1996) pp. 111–141.Google Scholar
  3. 3.
    R. J. R. Abel and M. Greig, BIBDs with small block size, in: CRC Handbook of Combinatorial Designs (C. J. Colbourn and J. H. Dinitz, eds.), CRC (1996) pp. 41–47.Google Scholar
  4. 4.
    R. J. R. Abel and M. Greig, Resolvable balanced incomplete block designs with a block size of 8, preprint.Google Scholar
  5. 5.
    R. J. R. Abel and W. H. Mills, Some new BIBDS with k = 6 and λ = 1, J. Combinatorial Designs, Vol. 3 (1995) pp. 381–391.Google Scholar
  6. 6.
    L. M. Batten, Linear spaces with line range {n − 1, n, n + 1} and at most n 2 points, J. Austral. Math. Soc. (A), Vol. 30 (1980) pp. 215–228.Google Scholar
  7. 7.
    F. E. Bennett, C. J. Colbourn and R. C. Mullin, Quintessential pairwise balanced designs, preprint.Google Scholar
  8. 8.
    T. Beth, D. Jungnickel and H. Lenz, Design Theory, Cambridge University Press, Cambridge, England (1986).Google Scholar
  9. 9.
    C. J. Colbourn and J. H. Dinitz, Making the MOLS table, Constructive and Computational Design Theory, Kluwer Academic Press (to appear).Google Scholar
  10. 10.
    C. J. Colbourn, J. H. Dinitz and M. Wojtas, Thwarts in transversal designs, Designs, Codes and Cryptography, Vol. 5 (1995) pp. 189–197.Google Scholar
  11. 11.
    S. Furino, J. Yin and Y. Miao, Frames and Resolvable Designs, CRC, Boca Raton, FL (to appear).Google Scholar
  12. 12.
    M. Greig, Design from projective planes, and PBD bases and designs from configurations in projective planes, unpublished, 1992.Google Scholar
  13. 13.
    A. M. Hamel, W. H. Mills, R. C. Mullin, R. Rees, D. R. Stinson and J. Yin, The spectrum of PBD(5,k b7,v) for k = 9, 13, Ars Combinatoria, Vol. 36 (1993) pp. 7–26.Google Scholar
  14. 14.
    H. Lenz, Some remarks on pairwise balanced designs, Mitt. Math. Sem. Giessen, Vol. 165 (1984) pp. 49–62.Google Scholar
  15. 15.
    A. C. H. Ling and C. J. Colbourn, Deleting lines in projective planes, Ars Combinatoria (to appear).Google Scholar
  16. 16.
    R. C. Mullin, B. Gardner, K. Metsch and G. H. J. van Rees, Some properties of finite bases for the Rosa set, Utilitas Mathematica, Vol. 38 (1990) pp. 199–215.Google Scholar
  17. 17.
    R. C. Mullin and H. D. O. F. Gronau, PBDs: recursive constructions, CRC Handbook of Combinatorial Designs (C. J. Colbourn and J. H. Dinitz, eds.), CRC (1996) pp. 193–203.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Alan C. H. Ling
    • 1
  • Xiaojun Zhu
    • 1
  • Charles J. Colbourn
    • 2
  • Ronald C. Mullin
    • 2
  1. 1.Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

Personalised recommendations