Improved lower bound on the size of Kakeya sets over finite fields

By Shubhangi Saraf, Madhu Sudan. 2008

63 citations recorded by the source corpus.

In 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 $\beta^n |\F|^n$ for a constant $\beta > 0$. This pins down the growth of the leading constant to the right form as a function of $n$.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f9021403ae9d691fc467b5d4a251e6e17ade5e5c