How to guess two letters correctly (Q1194746)

A set \(U\) of functions from \([k]\) to \([n]\) is called \((m,n,k)\)-guessing (where \(n,m,k\in\mathbb{N}\) and \(2\leq m\leq k)\), if for every function \(w\) from a subset of size \(m\) of \([k]\) into \([n]\) there exists a function in \(U\) coinciding with \(w\) in at least two places. Let \(g(m,n,k)\) denote the minimum size of an \((m,n,k)\)-guessing set. The authors estimate \(g(m,n,k)\), and in particular \(g(2,n,k)\) and \(g(k,n,k)\).