Cleaning a No Wax Floor?

We had a no wax Armstrong floor laid in our kitchen last fall. The pattern is a black and white diamond pattern. The black pattern is no problem it doesn't show the dirt, but on the white pattern we have tried everything to get it clean, nothing works! This floor has a rough surface to it that actually has little craters in the flooring. The dirt gets in the craters and we can't get it out. We are very discouraged with this floor! Is there any way to clean and then seal this type of floor to stop dirt from accumulating in the small craters?

By Richard M.