Minimal Completely Separating Systems of k-Sets

Let n and k be fixed positive integers. A collection C of k-sets of [n] is a completely separating system if, for all distinct i, j∈[n], there is an S∈C for which i∈S and j∉S. Let R(n, k) denote the minimum size of such a C. Our results include showing that if nk is a sequence with k⪡nk⪡k1+ε for every ε>0, then[formula]