Abstract
For two association schemes χ and χ', defined on the same set, we call χ' a subscheme of χ if each relation of χ' is a union of some relations of χ. In this paper we prove that the Johnson scheme J (v, d ) has no non-trivial subscheme if $v>2d+¥frac{3}{2}+¥sqrt{(d-¥frac{7}{2})^2+6}$. This slightly improves the earlier result of Muzichuk that the conclusion holds if v ≥ 3d + 4.
