2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167410In a recent breakthrough, Dvir showed that every Kakeya set in $\F^n$ must be of cardinality at least $c_n |\F|^n$ where $c_n \approx 1/n!$. We improve this lower bound to $β^n |\F|^n$ for a constant $β> 0$. This pins down the growth of the leading constant to the right form as a function of $n$.4 pages, Appendix with upper bound addedCombinatoricstext