  A hypergraph is said to be properly 2-colorable if there exists a 2-coloring
of its vertices such that no hyperedge is monochromatic. On the other hand, a
hypergraph is called non-2-colorable if there exists at least one monochromatic
hyperedge in each of the possible 2-colorings of its vertex set. Let m(n)
denote the minimum number of hyperedges in a non-2-colorable n-uniform
hypergraph. Establishing the lower and upper bounds on m(n) is a well-studied
research direction over several decades. In this paper, we present new
constructions for non-2-colorable n-uniform hypergraphs. These constructions
improve the upper bounds for m(8), m(13), m(14), m(16) and m(17). We also
improve the lower bound for m(5).
