  Bollob\'as, Reed and Thomason proved every $3$-uniform hypergraph
$\mathcal{H}$ with $m$ edges has a vertex-partition $V(\mathcal{H})=V_1 \sqcup
V_2 \sqcup V_3$ such that each part meets at least
$\frac{1}{3}(1-\frac{1}{e})m$ edges, later improved to $0.6m$ by Halsegrave and
improved asymptotically to $0.65m+o(m)$ by Ma and Yu. We improve this
asymptotic bound to $\frac{19}{27}m+o(m)$, which is best possible up to the
error term, resolving a special case of a conjecture of Bollob\'as and Scott.
