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Combinatorica

, Volume 11, Issue 3, pp 207–218 | Cite as

The number oft-wise balanced designs

  • Charles J. Colbourn
  • Dean G. Hoffman
  • Kevin T. Phelps
  • Vojtěch Rödl
  • Peter M. Winkler
Article

Abstract

We prove that the number oft-wise balanced designs of ordern is asymptotically\(n\left( {(_t^n )/(t + 1)} \right)(1 + o(1))\), provided that blocks of sizet are permitted. In the process, we prove that the number oft-profiles (multisets of block sizes) is bounded below by\(\exp \left( {c_1 = \sqrt n \log n} \right)\) and above by\(\exp \left( {c_2 = \sqrt n \log n} \right)\) for constants c2>c1>0.

AMS subject classification (1980)

05 B 30 05 B 05 

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References

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Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • Charles J. Colbourn
    • 1
  • Dean G. Hoffman
    • 2
  • Kevin T. Phelps
    • 2
  • Vojtěch Rödl
    • 3
  • Peter M. Winkler
    • 3
  1. 1.Dept. of Combinatorics and OptimizationUniversity of WaterlooWaterlooCANADA
  2. 2.Dept. of Alg., Combin. and AnalysisAuburn UniversityAuburnU.S.A.
  3. 3.Department of MathematicsEmory UniversityAtlantaU.S.A.

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