Tight relative 2-designs on two shells in Johnson association schemes

There exist many tight relative 2-designs on two shells in binary Hamming association schemes H(n,2)H(n,2) and each such design has the structure of a coherent configuration. In this paper, we study the existence problem of tight relative 2-designs on two shells in Johnson association schemes J(v,k)J(v,k). We determine all possible parameters of such designs for v≤100v≤100. For each case, we discuss whether such a design exists. Moreover, we construct some new tight relative 2-designs with constant weight in J(v,k)J(v,k). They are related to some specific symmetric 2-designs. All examples satisfying v≤100v≤100 have the structure of a coherent configuration.