The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. https://en.m.wikipedia.org/wiki/Miller_index
Does this mean, that parallel planes are generally equivalent, particularly does $(200)$ for example even exist or is this a wrong notation of $(100)$?
Also what is the correct notation for $(\bar{1}00)$? Since $(100)$ is parallel to $(\bar{1}00)$ I think $(100)$ is correct. Is there kind of a rule or a convention to invert the signs to obtain the maximum positive indices?