<p>We explore the well-known max hypergraph bisection problem, which is widely used in fields such as very large-scale integration layout design, network planning, biological networks and quantum computing. Given a hypergraph <i>H</i> = (<i>V</i>, <i>E</i>, <i>ω</i>) with a non-negative weight function <i>ω</i>: <i>E</i> → ℝ_⩾0, the goal is to find a balanced partition (<i>V</i>₁, <i>V</i>₂) while maximizing the total weight of hyperedges crossing different vertex subsets. For this purpose, we relax the max hypergraph bisection problem using the Lasserre hierarchy semidefinite programming. Then we design a new approximation algorithm combining random hyperplane and perturbation, and analyze the approximation factor via reducing dimensions and using interval arithmetic. Finally, we prove that if all hyperedges contain at least 3 vertices, the approximation factor is 0.7728; otherwise, the approximation factor is 0.6818. To the best of our knowledge, these results are the current best ones.</p>