On flag-transitive and point-primitive symmetric $$(v,k,\lambda )$$ designs of affine type with $$\lambda \leqslant 10$$

In this article, we investigate nontrivial symmetric (v,k,lambda) designs with lambda <= 10 admitting a flag-transitive and point-primitive affine automorphism group. In conclusion, all symmetric (v,k,lambda) designs admitting flag-transitive automorphism groups are known apart from those admitting one-dimensional automorphisms, and hence the classification of flag-transitive symmetric (v,k,lambda) designs with lambda <= 10 reduces to the case of one-dimensional affine automorphism groups.