35 mm can be sharp at a reasonable viewing distance at 16x20. Grain free...no. Can you do it with a consumer zoom lens...probably not. At 16x20 and 35mm you need to use the best lenses (enlarging and taking) and the best technique if you want a reasonably sharp result.
The question I ask is whether it is really necessary for all the reasons mentioned above. I have always questioned the need to print large anyway. An artist friend of mine told me about a saying in art school. If you can't make it good, make it red. If you can't make it red, make it big. I think there is a bit of that in the photography world too.