Yes, using an open (infinite) one dimensional low-discrepancy sequence in conjunction with a space-filling curve such as the Hilbert-curve has been explored. For example by Owen [1]
Niederreiter himself has a beautiful paper that includes a section on weighted low discrepancy sequence [2] where he also cites several references within it that might be of interest to you.
Niederreiter himself has a beautiful paper that includes a section on weighted low discrepancy sequence [2] where he also cites several references within it that might be of interest to you.
[1] http://statweb.stanford.edu/~owen/reports/extgrid.pdf [2] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.614...