  We have performed a 70 billion dark-matter particles N-body simulation in a 2
$h^{-1}$ Gpc periodic box, using the concordance, cosmological model as favored
by the latest WMAP3 results. We have computed a full-sky convergence map with a
resolution of $\Delta \theta \simeq 0.74$ arcmin$^{2}$, spanning 4 orders of
magnitude in angular dynamical range. Using various high-order statistics on a
realistic cut sky, we have characterized the transition from the linear to the
nonlinear regime at $\ell \simeq 1000$ and shown that realistic galactic
masking affects high-order moments only below $\ell < 200$. Each domain
(Gaussian and non-Gaussian) spans 2 decades in angular scale. This map is
therefore an ideal tool for testing map-making algorithms on the sphere. As a
first step in addressing the full map reconstruction problem, we have
benchmarked in this paper two denoising methods: 1) Wiener filtering applied to
the Spherical Harmonics decomposition of the map and 2) a new method, called
MRLens, based on the modification of the Maximum Entropy Method on a Wavelet
decomposition. While the latter is optimal on large spatial scales, where the
signal is Gaussian, MRLens outperforms the Wiener method on small spatial
scales, where the signal is highly non-Gaussian. The simulated full-sky
convergence map is freely available to the community to help the development of
new map-making algorithms dedicated to the next generation of weak-lensing
surveys.
