ON THE SYMMETRIC BLOCK DESIGN WITH PARAMETERS
(231,70,21) ADMITTING A GROUP OF ORDER 23

Abstract

In this paper we have proved that up to isomorphism there are at least eighty-six orbit structures for a putative symmetric block design D with parameters (231,70,21), admitting a group G of order 23.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 3
Year: 2018

DOI: 10.12732/ijam.v31i3.8

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References

  1. [1] M. Aschbacher, On collineation groups of symmetric block designs, J. Comb. Theory Ser. A, 11 (1971), 272-281.
  2. [2] T. Beth, D. Jungnickel and H. Lenz, Design Theory, Bibliographisches Institut, Mannheim-Wien-Z¨urich (1999).
  3. [3] A. Beutelspacher, Einfuhrung in die endliche Geometrie I, Bibliographisches Institut, Mannheim-Wien-Zurich (1985).
  4. [4] V. Cepulic, On symmetric block designs (40, 13, 4) with automorphisms of order 5, Discrete Math., 28, No 1-3 (1994), 45-60.
  5. [5] D. Crnkovic, Some new Menon designs with parameters (196,91,42), Mathematical Communications, 10, No 2 (2005), 169-175.
  6. [6] R. Gjergji, On the symmetric block design with parameters (153, 57, 21), Le Matematiche, 64, No 1 (2009), 147-159.
  7. [7] M. Gashi, A construction of a symmetric design with parameters (195,97,48) with help of Frobenius group of order 4656, International Mathematical Forum, 5, No 8 (2010), 383-388.
  8. [8] Z. Janko and Tran van Trung, Construction of a new symmetric block design for (78, 22, 6) with help of tactical decompositions, J. Comb. Theory, Ser. A, 40 (1995), 451-455.
  9. [9] Z. Janko, Coset enumeration in groups and constructions of symmetric designs, Combinatorics, 90 (1992), 275-277.
  10. [10] C.W.H. Lam, The search for a finite projective plane of order 10, Amer. Math. Monthly, 98 (1991), 305-318.
  11. [11] E. Lander, Symmetric Designs: An Algebraic Approach, Cambridge University Press (1983).