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<p>We consider certain 2-designs arising from finite fields. The maximal number in the intersections of any two distinct blocks in such a 2-design is shown to depend solely on the characteristic of the finite field and the block size of the design. A characterization and an algorithm are given to determine the maximal number of intersection points when the finite field and block size of such a 2-design are given.</p>

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Intersection Numbers of Certain 2-Designs from Finite Fields

  • 期刊论文

  • 发表日期：

    2025年3月5日

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  • Tim Boykett,
  • Po-Yi Huang,
  • Wen-Fong Ke,
  • Hubert Kiechle,
  • Günter F. Pilz

摘要

We consider certain 2-designs arising from finite fields. The maximal number in the intersections of any two distinct blocks in such a 2-design is shown to depend solely on the characteristic of the finite field and the block size of the design. A characterization and an algorithm are given to determine the maximal number of intersection points when the finite field and block size of such a 2-design are given.