  Permutation polynomials with few terms (especially permutation binomials)
attract many people due to their simple algebraic structure. Despite the great
interests in the study of permutation binomials, a complete characterization of
permutation binomials is still unknown. In this paper, we give a classification
of permutation binomials of the form $x^i+ax$ over $\mathbb{F}_{2^n}$, where
$n\leq 8$ by characterizing three new classes of permutation binomials. In
particular one of them has relatively large index $\frac{q^2+q+1}{3}$ over
$\mathbb{F}_{q^3}$.
