  Bisch and Jones proposed the classification of planar algebras by simple
generators and relations. In this paper, we study the generating problem for a
family of group-subgroup subfactors associated with the Kneser graphs, namely,
to determine the generators with minimal size. In particular, we prove that
this family of subfactors are generated by $2$-boxes and this provides an
affirmative answer to a question of Vaughan Jones. This generator problem is
also related to the theory of quantum permutation groups, and the main theorem
also provides an infinite family of strongly regular graphs with no quantum
symmetry.
