Euclid Preparation XXIX: Forecasts for 10 different higher-order weak lensing statistics

This paper presents the HOWLS data set and first results. Are released with the paper the 512 convergence maps computed from the DUSTGRAIN-pathfinder simulations varying Omega_m and sigma_8, and the 924 convergence maps computed from the SLICS simulations. We also display the data vectors that are used in the analysis as well as the inverse Fisher matrix (corrected for the Sellentin & Heavens factor, see paper for details) for the shear and convergence two-point correlation functions, one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, scattering transform coefficients, high-order moments, and third and n-th aperture mass statistics. These data should allow external researchers to reproduce our results and to test their own implementation of higher-order statistics and compare it with our forecasts.