Application icons is pixelated

I'm trying to set an icon for my app, however the icons derived from the original image is pixelated and looks bad, I tried to provide the app icon gear application with images of different sizes, however the result is still unpleasant! Should I provide it with images of higher resolution or lower resolution to get better results? In the question in the link under there's an answer providing a matrix provided by Apple for icon sizes. My question is, should I use these sizes strictly, or consider them as a lower border not to go under, or consider them as a ceiling not to exceed? the question's link