2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103696A two-dimensional Besicovitch set over a finite field is a subset of the finite plane containing a line in each direction. In this paper, we conjecture a sharp lower bound for the size of such a subset and prove some results toward this conjecture.9 pages; added mention of an alternate proof of the Incidence Formula; included mention of the recent related result of Joshua Cooper. to appear in "Journal of Number Theory"Number Theory05B25; 11T99text