On the parameters of two-intersection sets in PG(3, q)

Stefano Innamorati, Fulvio Zuanni

Abstract


In this paper we study the behaviour of the admissible parameters of a two-intersection set in the finite three-dimensional projective space of order q=ph a prime power. We show that all these parameters are congruent to the same integer modulo a power of p. Furthermore, when the difference of the intersection numbers is greater than the order of the underlying geometry, such integer is either 0 or 1 modulo a power of p. A useful connection between the intersection numbers of lines and planes is provided. We also improve some known bounds for the cardinality of the set. Finally, as a by-product, we prove two recent conjectures due to Durante, Napolitano and Olanda.

Keywords


Set of Type (m, n)_2; Two-Character Set; Two-Intersection Set

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DOI: http://dx.doi.org/10.1478/AAPP.96S2A7

Copyright (c) 2018 Stefano Innamorati, Fulvio Zuanni

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