The state-of-art radiative magnetohydrodynamical codes (eg. MURaM and BIFROST) use a quadrature known as Set A by Carlson (1963). The advantage of this particular quadrature is that it is invariant with respect to 90

^{o}axis rotation.

**Terminology**

The quadrature is defined by directional cosines $\mu_l$ and their weights $w_l$. They are combined into sets that define rays $\Omega_m = (\mu_x, \mu_y, \mu_z)$ and their weights $w_m$. The order of quadrature $n$ specifies the number of $\mu$ levels in the [-1, 1] interval. Since the quadrature is symmetric in respect to axis, it is sufficient to find values of the angles in half of that range. Thus the number of $\mu$ levels is $l_{max} = n/2$. The number of rays per octant in this scheme is $n(n+2)/8$. Each ray is labeled by three numbers indexing $\mu$ level along one of the axes. The sum of indices of a ray is the same of all rays, $l_{max}+2$. For example, when $n=8$ and $l_{max}=4$, possible indices are 1, 2, 3 and 4. Their possible variations are those that have sum of 6. The number of these variations (and the rays) is $n(n+2)/8 = 10$. The number of different classes (variation without repetition with the specified sum) is $l_{max}-1 = 3$. In our example: (4, 1, 1), (3, 2, 1) and (2, 2, 2).