On the Minimum Size of Linear Sets - Adriaensen, Sam; Santonastaso, Paolo (The Electronic Journal of Combinatorics, 2024)
Recently, a lower bound on the size of linear sets in projective spaces intersecting a hyperplane in a canonical subgeometry was established. There are several constructions showing that this bound is tight. In this paper, we generalize this bound to linear sets meeting some subspace π in a canonical subgeometry. We obtain a tight lower bound on the size of any F_q-linear set spanning PG(d,q^n) in case that n ≤ q and n is prime. We also give constructions of linear sets attaining equality in the former bound, both in the case that π is a hyperplane, and in the case that π is a lower dimensional subspace.