The number of designs with geometric parameters grows exponentially View Full Text


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Article Info

DATE

2009-05-23

AUTHORS

Dieter Jungnickel, Vladimir D. Tonchev

ABSTRACT

It is well-known that the number of 2-designs with the parameters of a classical point-hyperplane design PGn-1(n, q) grows exponentially. Here we extend this result to the number of 2-designs with the parameters of PGd(n, q), where 2 ≤ d ≤ n − 1. We also establish a characterization of the classical geometric designs in terms of hyperplanes and, in the special case d = 2, also in terms of lines. Finally, we shall discuss some interesting configurations of hyperplanes arising in designs with geometric parameters. More... »

PAGES

131-140

References to SciGraph publications

  • 2008-11-26. Polarities, quasi-symmetric designs, and Hamada’s conjecture in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1993-05. Some characterizations of quasi-symmetric designs with a spread in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2002-10. A New Bound on the Number of Designs with Classical Affine Parameters in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1994-07. Automorphisms and Isomorphisms of Symmetric and Affine Designs in JOURNAL OF ALGEBRAIC COMBINATORICS
  • 1984-06. The number of designs with classical parameters grows exponentially in GEOMETRIAE DEDICATA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10623-009-9299-6

    DOI

    http://dx.doi.org/10.1007/s10623-009-9299-6

    DIMENSIONS

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