  In a recent result, Khot and Saket [FOCS 2014] proved the quasi-NP-hardness
of coloring a 2-colorable 12-uniform hypergraph with $2^{(\log n)^{\Omega(1)}}$
colors. This result was proved using a novel outer PCP verifier which had a
strong soundness guarantee. In this note, we show that we can reduce the arity
of their result by modifying their 12-query inner verifier to an 8-query inner
verifier based on the hypergraph coloring hardness reductions of Guruswami et.
al. [STOC 2014]. More precisely, we prove quasi-NP-hardness of the following
problems on n-vertex hypergraphs.
  - Coloring a 2-colorable 8-uniform hypergraph with $2^{(\log n)^{\Omega(1)}}$
colors.
  - Coloring a 4-colorable 4-uniform hypergraph with $2^{(\log n)^{\Omega(1)}}$
colors.
