Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold

It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in P⁴ (Fq²) has at most d(q⁵+q²) + q³ + 1 points in common with a threefold of degree d defined over Fq². He proved the conjecture for $d=2$. In this paper, we show that the conjecture is true for $d = 3$ and q ≥ 7.