Timeline for Blocking sets in three dimensional finite affine spaces

4 events

when toggle format	what		by	license	comment
Jan 27, 2016 at 22:57	comment	added	Anurag		I would like to add that a friend of mine is running a computation which has shown that $s(4) = 34 < 36$ (in case you are wondering about the sharpness of this bound $s(q) \leq 3q^2 - 3q$). He'll hopefully post more values he has computed by tomorrow. By interpolating from $s(2), s(3), s(4)$ we could make a bold (and probably wrong) conjecture that $s(q) = (5q^2 - 3q)/2$ ... But may be one can try constructing examples of size $(5q^2 - 3q)/2$ to show $s(q) \leq (5q^2 - 3q)/2$.
Jan 27, 2016 at 22:51	comment	added	Anurag		Thanks. This is how I understand the second part: all lines contained in the hyperplanes $H_1, \dots, H_q$ are blocked once you have chosen a pair of intersecting lines in each of them. And every transverse which doesn't contain $P$ is blocked by $H_1 \setminus \{P\}$. Any transverse through $P$ other than the line $\ell$ intersects every $H_i$ ($i > 2$) in a point $R_i$ other than $Q_i = \ell \cap H_i$ and the line $Q_iR_i$ is parallel to one of the $q+1$ lines through $P$ in $H_1$. So, we ensure that for each line through $P$ in $H_1$, we take a parallel line through $Q_i$ in $H_i$.
Jan 27, 2016 at 22:08	history	edited	Douglas Zare	CC BY-SA 3.0	Added upper bound.
Jan 27, 2016 at 20:09	history	answered	Douglas Zare	CC BY-SA 3.0