Uniform distribution conjecture for the interlaced Halton sequence

Let the $d$-dimensional interlaced Halton sequence be the sequence constructed by Algorithm. A sequence $(\mathbf{x}_n)_{n\geq 0}$ in $[0,1)^d$ is uniformly distributed if, for every axis-parallel box $B\subseteq[0,1)^d$, the proportion of its first $N$ points lying in $B$ converges to the volume of $B$ as $N\to\infty$.

Uniform distribution conjecture. The $d$-dimensional interlaced Halton sequence in Algorithm is uniformly distributed.

The construction is intended to provide a higher-dimensional sequence with more uniform projections than the classical Halton sequence. The source gives no proof or resolution of this conjecture.