Minimal linear spaces

A decent linear space DLS(k) is a linear space with minimal line size at least three and with maximal line size exactly k. Denote by vk (resp. bk) the minimum number of points (resp. lines) in a DLS(k). We determine the numbers vk and bk for all k and prove that each DLS(k) with bk lines has vk points. Thus the DLS(k)'s with bk lines are the minimal linear spaces.