is generated for $\Lambda$CDM7 using the COSMICS package [@cosmics]. Further, we work with a parametric form of the power spectrum taken from [@EH98] (eqs. 29-31 in their paper)

For  we still need to construct the basis velocity fields $\vv^\alpha(\vx)$. Here we use $N_{\rm a}=120 $ basis functions, extracted in a similar way to the mocks, but from a completely different random realisation of a velocity field in a very large box. Thanks to the regularization term in (\[eq:chi\]), the  inferred bulk flow has very little dependence on the actual value of $N_{\rm a}$ as long as it is large enough to capture the main features of the 3D flow: very similar results are obtained with $N_{\rm a}=50$ and $N_{\rm a}=120$. Each of these 120 velocity fields $\vv^\alpha(\vx)$ are further smoothed with a gaussian window of $10\hmpc$ in width. The purpose of this small scale smoothing is to filter out low frequency modes which would be over-fitted by the data especially at large distances. This smoothing, however, has very little effect on the bulk flows reconstructed by . We emphasize that a basis function $\vv^\alpha(\vx)$ is not only defined at the galaxy positions, but also at any point in a sufficiently 