  We generalize a Furstenberg-type result of Orponen-Shmerkin to higher
dimensions, leading to an $\epsilon$-improvement in Kaufman's projection
theorem for hyperplanes and an unconditional discretized radial projection
theorem in the spirit of Orponen-Shmerkin-Wang. Our proof relies on a new
incidence estimate for $\delta$-tubes and a quasi-product set of $\delta$-balls
in $\mathbb{R}^d$.
