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We show how to construct a non-2-colorable k-uniform hypergraph with (2^(1 +o(1)))^k edges. By the duality of hypergraphs and monotone k-CNF-formulas thisgives an unsatisfiable monotone k-CNF with (2^(1 + o(1)))^k clauses

Construction of a Non-2-colorable k-uniform Hypergraph with Few Edges