  Let $\mathbb{F}_q$ denote a finite field of $q$ elements. Define a set
$B\subset\mathbb{F}_q^n$ to be Nikodym if for each $x\in B^{c}$, there exists a
line $L$ such that $L\cap B^c=\{x\}.$ The main purpose of this note is to show
that the size of every Nikodym set is at least $C_n\cdot q^n$, where $C_n$
depends only on $n$.
