Density of Balanced 3-Partite Graphs without 3-Cycles or 4-Cycles

Let $C_k$ be a cycle of order $k$, where $k\ge 3$. ex$(n, n, \{C_{3}, C_{4}\})$ the maximum number edges in balanced $3$-partite graph whose vertex set consists three parts, each has $n$ vertices that no subgraph isomorphic to $C_3$ or $C_4$. We construct dense 3-partite graphs without 3-cycles 4-cycles and show C_{4}\})\ge (\frac{6\sqrt{2}-8}{(\sqrt{2}-1)^{3/2}}+o(1))n^{3/2}$.