sobol_sequence

First N points of the d-dimensional Sobol sequence (Bratley-Fox direction numbers), via the direct formula

x_n = XOR_{c : bit c of gray(n+1) is set} V[:, c]     (n = 0..N-1)

where gray(k) = k XOR (k » 1). This 0-indexed convention matches the classic Fortran/MATLAB/Python reference implementations (Burkardt et al.) exactly – validated against that reference in main below.