The number oft-wise balanced designs

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.

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Colbourn, C.J., Hoffman, D.G., Phelps, K.T. et al. The number oft-wise balanced designs. Combinatorica 11, 207–218 (1991). https://doi.org/10.1007/BF01205073

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AMS subject classification (1980)

  • 05 B 30
  • 05 B 05