  We improve upon the lower bound for 3-colour hypergraph Ramsey numbers,
showing, in the 3-uniform case, that \[r_3 (l,l,l) \geq 2^{l^{c \log \log
l}}.\] The old bound, due to Erd\H{o}s and Hajnal, was \[r_3 (l,l,l) \geq 2^{c
l^2 \log^2 l}.\]
