Timeline for Largest number of points one can pick in finite projective space without getting three on a line
Current License: CC BY-SA 3.0
7 events
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| Aug 15, 2017 at 10:16 | comment | added | DavidButlerUofA | Also worth noting if you want to search for papers, that often they are called k-arcs (for n=2) or k-caps (for n > 2). | |
| Aug 15, 2017 at 6:31 | comment | added | DavidButlerUofA | Yes that paper is about the same things. $PG(n,q)$ is what the OP calls "$\mathbb{PF}_q^n$". See also this very recent paper from JA Thas arxiv.org/abs/1702.01097 | |
| Aug 14, 2017 at 23:55 | vote | accept | forget this | ||
| Aug 14, 2017 at 23:20 | comment | added | Gro-Tsen | @user193072 This paper (Storme, Thas & Vereecke, "New Upper bounds for the sizes of caps in finite projective spaces" J. Geometry 73 (2002) 176–193) seems to be about this, although I will admit that this is just what Google turned up and I looked no further than the abstract). | |
| Aug 14, 2017 at 23:01 | comment | added | forget this | Thank you! A great answer. Is anything non-trivial known about upper bounds? | |
| Aug 14, 2017 at 22:17 | history | edited | Gro-Tsen | CC BY-SA 3.0 |
mention the $n=2$ case and the related theorem by B. Segre
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| Aug 14, 2017 at 22:09 | history | answered | Gro-Tsen | CC BY-SA 3.0 |