In one dimension d=1 an equally-spaced set of N points in [0,1) has the lowest possible (star) discrepancy D=0.5/N. Unfortunately, I found only asymptotic bounds for other dimensions (e.g. acc. to Schmidt and Roth). These best-known lower bounds are so bad (also they are known to be "tight"), that for moderate N and d (like N=10..1000 and d=2) they can be off by a factor of 10 or more.
I would like to have a table D vs N and d (or formulas) for comparing D for the best-known low-discrepancy sets, e.g. against regular grids (for which an exact formula exists) or random sets (here I also found no formula, and simply creating a rnd set and calculating D is also extremely time-consuming.
Actually, I am very suprised because at least for d=2 a Fibonacci set delivers a very low, almost perfect discrepancy, so very low errors for Monte-Carlo integration.