Vol. 1, No. 3, 2008

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
An improved lower bound on the size of Kakeya sets over finite fields

Shubhangi Saraf and Madhu Sudan

Vol. 1 (2008), No. 3, 375–379
Abstract

In a recent breakthrough, Dvir showed that every Kakeya set in Fn must have cardinality at least cn|F|n, where cn 1n!. We improve this lower bound to βn|F|n for a constant β > 0. This pins down the correct growth of the constant cn as a function of n (up to the determination of β).

Keywords
Kakeya set, finite fields, polynomial method
Mathematical Subject Classification 2000
Primary: 52C17
Secondary: 05B25
Milestones
Received: 22 August 2008
Revised: 23 September 2008
Accepted: 22 October 2008
Published: 18 December 2008
Authors
Shubhangi Saraf
Massachusetts Institute of Technology
Computer Science and Artificial Intelligence Laboratory
32 Vassar Street
Cambridge, MA 02139
United States
Madhu Sudan
Massachusetts Institute of Technology
Computer Science and Artificial Intelligence Laboratory
32 Vassar Street
Cambridge, MA 02139
United States