  In 1964 Erd\H{o}s proved, by randomized construction, that the minimum number
of edges in a $k$-graph that is not two colorable is $O(k^2\; 2^k)$. To this
day, it is not known whether there exist such $k$-graphs with smaller number of
edges. Known deterministic constructions use much larger number of edges. The
most recent one by Gebauer requires $2^{k+\Theta(k^{2/3})}$ edges. Applying
derandomization technique we reduce that number to
$2^{k+\widetilde{\Theta}(k^{1/2})}$.
