The classical and naïve procedure for generating Poisson Hypersphere samples is by acceptance rejection, which has complexity over $O(N^2)$ and is thus unfeasible for most practical usage with on-the-fly generation. This cost could be improved by space partitioning techniques at low dimensions, but at high ones afaik they become useless again with uniform distributions.
Poisson disc sampling is thus not used widely beyond dimension 10, and I fear in general it is not a meaningful method in high dimensions because of geometric issues, which are conveniently bypassed by standard low discrepancy sequences (e.g. the fact that most of the hypercube volume is near the boundary).
Another drawback w.r.t. some quasi-MC sequences is that smoothness of the integrand is not exploited and thus convergence can be significantly slower.
Similar in spirit is optimal quantization which is performed on arbitrary nonuniform distributions (by Pages, Callegaro &c). It has useful properties but suffers from even worse practical drawbacks (often points must be precomputed).
Imho the way to go is quasi-MC, there are sophisticated modern methods which beat anything else by a wide margin, in particular when used with proper integrand adaptations.