Designs, Codes and Cryptography

, Volume 27, Issue 1–2, pp 131–137 | Cite as

Enumeration of 2-(9, 3, λ) Designs and Their Resolutions

  • Patric R. J. Östergård
  • Petteri Kaski
Article

Abstract

We consider 2-(9, 3, λ) designs, which are known to exist for all λ ≥ 1, andenumerate such designs for λ = 5 and their resolutions for 3 ≤ λ ≤ 5, the smallestopen cases. The number of nonisomorphic such structures obtained is 5 862 121 434, 426, 149 041, and 203 047732, respectively. The designs are obtained by an orderly algorithm, and the resolutions by two approaches:either by starting from the enumerated designs and applying a clique-finding algorithm on two levels or by anorderly algorithm.

automorphism group BIBD oderly algorithm resolved design 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Patric R. J. Östergård
    • 1
  • Petteri Kaski
    • 2
  1. 1.Department of Electrical and Communications EngineeringHelsinki University of TechnologyHUTFinland
  2. 2.Department of Computer Science and EngineeringHelsinki University of TechnologyHUTFinland

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