  The problem of 2-coloring uniform hypergraphs has been extensively studied
over the last few decades. An n-uniform hypergraph is not 2-colorable if its
vertices can't be colored with two colors, Red and Blue, such that every
hyperedge contains Red as well as Blue vertices. The least possible number of
hyperedges in an n-uniform hypergraph which is not 2-colorable is denoted by
m(n). In this paper, we consider the problem of finding an upper bound on m(n)
for small values of n. We provide constructions which improve the existing
results for some such values of n. We obtain the first improvement in the case
of n=8.
