A $t$-intersecting constant dimension subspace code $C$ is a set of $k$-dimensional subspaces in a projective space PG(n,q), where distinct subspaces intersect in a $t$-dimensional subspace. A classical example of such a code is the sunflower, where all subspaces pass through the same $t$-space. The sunflower bound states that such a code is a sunflower if $|C| > \left( \frac { q^{ k + 1} - q^{ t + 1}}{ q - 1} \right)^2 + \left( \frac { q^{ k + 1} - q^{ t + 1}}{ q - 1} \right) + 1$. In this article we will look at the case $t=0$ and we will improve this bound for $q\geq 9$: a set $\mathcal{ S}$ of $k$-spaces in PG(n,q), $q\geq 9$, pairwise intersecting in a point is a sunflower if $|\mathcal{ S}|> \left(\frac{ 2}{ \sqrt[6]{ q}}+\frac{ 4}{ \sqrt[3]{ q}}-\frac{ 5}{ \sqrt{ q}}\right)\left(\frac { q^{ k + 1} - 1}{ q - 1}\right)^2$.
Categories: math.CO