A $t$-fold packing of a projective space $\rm{ PG}_n(q)$ is a collection $\mathcal{ P}$ of line-spreads such that each line of $\rm{ PG}_n(q)$ occurs in precisely $t$ spreads in $\mathcal{ P}$. A $t$-fold packing $\mathcal{ P}$ is transitive if a subgroup of $\rm{ P\Gamma L}_{ n+1}(q)$ preserves and acts transitively on $\mathcal{ P}$. We give a construction for a transitive $(q-1)$-fold packing of $\rm{ PG}_n(q)$, where $q=2^k$, for any odd positive integers $n$ and $k$, such that $n\geq 3$. This generalises a construction of Baker from 1976 for the case $q=2$.
Categories: math.CO