"There is no factory here."
Translation:Здесь нет завода.
In the English, "There is" is a kind of token or place-holder designed to give the sentence a complete structure. It doesn't mean a particular place or direction, but in English, we're not comfortable saying "No factory here."
The phrase "There is" isn't actually in the Russian sentence, except as might be understood by a native-speaker, but I don't know if that's the case.
Там is an actual place or direction. If you included it in the sentence, you'd created ambiguity and conflict, because of the other place or direction, здесь = "here". The factory can't be both "here" and "there" at the same time, so там is wrong because we're talking about "here" not "there".