Key points are not available for this paper at this time.
A Diophantine m-tuple over a finite field Fq is a set \a₁, , aₘ\ of m distinct elements in Fₐ^* such that a₈a₉+1 is a square in Fq whenever i j. In this paper, we study M (q), the maximum size of a Diophantine tuple over Fq, assuming the characteristic of Fq is fixed and q. By explicit constructions, we improve the lower bound on M (q). In particular, this improves a recent result of Dujella and Kazalicki by a multiplicative factor.
Kim et al. (Mon,) studied this question.