  For a given hypergraph $H = (V,E)$ consider the sum $q(H)$ of $2^{-|e|}$ over
$e \in E$. Consider the class of hypergraphs with the smallest edge of size $n$
and without a 2-colouring without monochromatic edges. Let $q(n)$ be the
smallest value of $q(H)$ in this class.
  We provide a survey of the known bounds on $q(n)$ and make some minor
refinements.
