Spanning Subspaces in Finite Field Vector Space

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Let $\mathbb{F}_q^m$ be vector space over $\mathbb{F}_q$. For a $k\geq m$ a set $A$ of vectors is called ``almost spanning'' if every subset $B\subseteq A$ with $|B|=k$ span the entire vector space, i.e.,

$$\text{span}(B) = \mathbb{F}_q^m.$$ What is the maximum size of $A$?