Regular sets and quasi-symmetric 2-designs

  • A. Neumaier
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 969)


The paper presents a classification of quasi-symmetric 2-designs, and sufficient parameter information to generate a list of all feasible "exceptional" parameter sets for such designs with at most 40 points. The main tool is the concept of a regular set in a strongly regular graph.


Adjacency Matrix Regular Graph Intersection Number Balance Design Lecture Note Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Beker and W. Haemers, 2-designs having an intersection number k-n, J. Combin. Theory (Ser. A) 28 (1980), 64–82.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    W.G. Bridges and M.S. Shrikhande, Special partially balanced incomplete block designs and associated graphs, Discrete Math. 9 (1974), 1–18.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    P.J. Cameron, Extending symmetric designs, J. Combin. Theory 14 (1973), 215–220.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    P.J. Cameron, Biplanes, Math. Z. 131 (1973), 85–101.CrossRefGoogle Scholar
  5. 5.
    P.J. Cameron and J.H. van Lint, Graphs, Codes and Designs. London Math.Soc. Lecture Note Series 43, Cambridge Univ. Press 1980.Google Scholar
  6. 6.
    P. Delsarte, An algebraic approach to the association schemes of coding theory, Phil. Res. Rep. Suppl. 10 (1973), 1–97.MathSciNetzbMATHGoogle Scholar
  7. 7.
    J.M. Goethals and J.J. Seidel, Strongly regular graphs derived from combinatorial designs, Can. J. Math. 22 (1970), 597–614.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    M. Hall, jr., and W.S. Connor, An embedding theorem for balanced incomplete block designs, Can. J. Math. 6 (1953), 35–41.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    X. Hubaut, Strongly regular graphs. Discrete Math. 13 (1975), 357–381.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    D.R. Hughes and F.C. Piper, On resolutions and Bose's theorem, Geom. dedicata 5 (1976), 129–133.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    A. Neumaier, Strongly regular graphs with smallest eigenvalue-m, Arch. Math. 33 (1979), 392–400.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    A. Neumaier, t 1/2-designs, J. Combin. Theory (Ser. A) 28 (1980), 226–248.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    A. Neumaier, Regular cliques in graphs and special 1 1/2-designs. In: Finite Geometries and Designs, London Math. Soc. Lecture Note Series 49, Cambridge Univ. Press 1981, pp. 244–259.Google Scholar
  14. 14.
    A. Neumaier, New inequalities for the parameters of an association scheme. In: Combinatorics and Graph Theory, Lecture Notes in Mathematics 885, Springer Verlag, 1981, pp. 365–367.Google Scholar
  15. 15.
    D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments. Wiley, New York 1971.zbMATHGoogle Scholar
  16. 16.
    J.J. Seidel, Strongly regular graphs, an introduction. In: Surveys in Combinatorics, London Math. Soc. Lecture Note Series 38, Cambridge Univ. Press 1979, pp. 157–180.Google Scholar
  17. 17.
    H.A. Wilbrink and A.E. Brouwer, A (57, 14, 1) strongly regular graph does not exist. Math. Centrum Report ZW 121/78, Amsterdam 1978.Google Scholar
  18. 18.
    E. Witt, Über Steinersche Systeme, Abh. Math. Sem. Hamburg Univ. 12 (1938), 265–275.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • A. Neumaier
    • 1
  1. 1.Institut für Angewandte Mathematik der Universität Freiburg i.Br.Freiburg i.Br.

Personalised recommendations