# smallest affine plane not generated by a field

What is the smallest affine plane not generated by a field? By "smallest" I mean has the least number of points. By "generated by a field", I mean planes of this form:

$X = \mathbb{F}^2$ (the set of points)
$$L = \{\{(x,ax+b) \mid x \in \mathbb{F} \} \mid a,b \in \mathbb{F}\} \cup \{ \{(x,y) \mid y \in \mathbb{F} \} \mid x \in \mathbb{F} \} \quad (\text{set of lines})$$ If you could list the lines as sets of points that would be ideal, thanks

Also if there are multiple smallest such planes, one example is sufficient