The characterization problem for designs with the parameters of AGd(n, q)

Abstract

We start a new characterization of the geometric 2-design AG d (n,q) among all simple 2-designs with the same parameters by handling the cases d ∈ {1,2,3,n — 2}. For d ≠ 1, our characterization is in terms of line sizes, and for d = 1 in terms of the number of affine hyperplanes. We also show that the number of non-isomorphic resolvable designs with the parameters of AG1(n,q) grows exponentially with linear growth of n.

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Correspondence to Dieter Jungnickel.

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In memoriam Hanfried Lenz

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Jungnickel, D., Metsch, K. The characterization problem for designs with the parameters of AGd(n, q). Combinatorica 36, 513–535 (2016). https://doi.org/10.1007/s00493-014-3212-2

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Mathematics Subject Classication (2000)

  • 05B05
  • 51E20