Abstract
Let \(\mathbb{F}\) be a finite field, and let (ℙ, B) be a nontrivial 2-(n, k, 1)-design over \(\mathbb{F}\). Then each point α∈ℙ induces a (k−1)-spread Sα on ℙ/α. (ℙ, B) is said to be a geometric design if Sα is a geometric spread on ℙ/α for each α∈ℙ. In this paper, we prove that there are no geometric designs over any finite field \(\mathbb{F}\).
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Research partially supported by NSF grant DMS-8703229.
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Thomas, S. Designs and partial geometries over finite fields. Geom Dedicata 63, 247–253 (1996). https://doi.org/10.1007/BF00181415
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DOI: https://doi.org/10.1007/BF00181415