Although using a low discrepancy sequence (eg Halton, Sobol, R2) might be a good starting point, these sequences are designed to maximize the distance between p

Although using a low discrepancy sequence (eg Halton, Sobol, R2) might be a good starting point, these sequences are designed to maximize the distance between points assuming that the left-and-right edges wrap, as well as the top-and-bottom. As it seems that the OP does not require this condition, I wold presume you get better solutions which involve lots of going to and from the far-left to the far-right, etc.. (Ordered dither matrices might offer another good starting point.)