Vector space partitions of $\mathrm{GF}(2{)}^8$

Abstract

A vector space partition $\mathcal{P}$ of the projective space $\mathrm{PG}(v-1,q)$ is a set of subspaces in $\mathrm{PG}(v-1,q)$ which partitions the set of points. We say that a vector space partition $\mathcal{P}$ has type $(v-1{)}^{m_{v-1}}\dots 2^{m_2}{1}^{m_1}$ if precisely $m_i$ of its elements have dimension $i$, where $1\le i\le v-1$. Here we determine all possible types of vector space partitions in $\mathrm{PG}(7,2)$.

27 pages