On the Ramsey numbers of daisies II

A $(k+r)$ -uniform hypergraph $H$ on $(k+m)$ vertices is an $(r,m,k)$ -daisy if there exists a partition of the vertices $V(H)=K\cup M$ with $|K|=k$ , $|M|=m$ such that the set of edges of $H$ is all the $(k+r)$ -tuples $K\cup P$ , where $P$ is an $r$ -tuple of $M$ . We obtain an $(r-2)$ -iterated exponential lower bound to the Ramsey number of an $(r,m,k)$ -daisy for $2$ -colours. This matches the order of magnitude of the best lower bounds for the Ramsey number of a complete $r$ -graph.