Improved upper bounds for partial spreads

Abstract

A partial $(k-1)$-spread in $\mathrm{PG}(n-1,q)$ is a collection of $(k-1)$-dimensional subspaces with trivial intersection, i.e., each point is covered at most once. So far the maximum size of a partial $(k-1)$-spread in $\mathrm{PG}(n-1,q)$ was known for the cases $n\equiv 0(\mathrm{mod}k)$, $n\equiv 1(\mathrm{mod}k)$ and $n\equiv 2(\mathrm{mod}k)$ with the additional requirements $q=2$ and $k=3$. We completely resolve the case $n\equiv 2(\mathrm{mod}k)$ for the binary case $q=2$.

8 pages

Cited by in corpus (7)

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• Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects
• A subspace code of size $333$ in the setting of a binary $q$-analog of the Fano plane