A note on lower bounds for hypergraph Ramsey numbers

We improve upon the lower bound for 3-colour hypergraph Ramsey numbers, showing, in the 3-uniform case, that r_(3)(l, l, l) ≥ 2^(l^(c log log l)). The old bound, due to Erdős and Hajnal, was r_(3)(l, l, l) ≥ 2^(cl^(2) log^(2) l).