Vector space partitions of GF(2)^8

Abstract

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