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

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=p^h 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.