Derandomizing Chernoff Bound with Union Bound with an Application to   $k$-wise Independent Sets
  Derandomization of Chernoff bound with union bound is already proven in many papers. We here give another explicit version of it that obtains a construction of size that is arbitrary close to the probabilistic nonconstructive size.   We apply this to give a new simple polynomial time constructions of almost $k$-wise independent sets. We also give almost tight lower bounds for the size of $k$-wise independent sets. 
Nader H. Bshouty
cs.DM