Quasi-symmetric 2, 3, 4-designs

Abstract

Quasi-symmetric designs are block designs with two block intersection numbersx andy It is shown that with the exception of (x, y)=(0, 1), for a fixed value of the block sizek, there are finitely many such designs. Some finiteness results on block graphs are derived. For a quasi-symmetric 3-design with positivex andy, the intersection numbers are shown to be roots of a quadratic whose coefficients are polynomial functions ofv, k and λ. Using this quadratic, various characterizations of the Witt—Lüneburg design on 23 points are obtained. It is shown that ifx=1, then a fixed value of λ determines at most finitely many such designs.

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Sane, S.S., Shrikhande, M.S. Quasi-symmetric 2, 3, 4-designs. Combinatorica 7, 291–301 (1987). https://doi.org/10.1007/BF02579306

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AMS subject classification (1980)

  • 05 B 05
  • 05 B 25