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An improved lower bound
on the size of Kakeya sets over finite fields
Shubhangi Saraf and Madhu Sudan |
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Vol. 1 (2008), No. 3, 375–379
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Abstract |
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In a recent breakthrough, Dvir showed that every Kakeya set in must have cardinality at least , where . We improve this lower bound to for a constant . This pins down the correct growth of the constant as a function of (up to the determination of ). |
Keywords
Kakeya set, finite fields, polynomial method
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Mathematical Subject Classification 2000
Primary: 52C17
Secondary: 05B25
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Milestones
Received: 22 August 2008
Revised: 23 September 2008
Accepted: 22 October 2008
Published: 18 December 2008
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Authors |
| Shubhangi Saraf | |
| Massachusetts Institute of
Technology Computer Science and Artificial Intelligence Laboratory 32 Vassar Street Cambridge, MA 02139 United States |
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| Madhu Sudan | |
| Massachusetts Institute of
Technology Computer Science and Artificial Intelligence Laboratory 32 Vassar Street Cambridge, MA 02139 United States |
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