What is rich base or richness of base? Thank you for your help I have found a lot of references to it but no clear definitions.
Richness of the Base (RotB) is a slogan referring to the fact that Optimality Theory only evaluates output, and has no mechanism for saying what things exist in inputs. This is in contrast with rules-based theories which has Morpheme Structure Constraints that could say e.g. "No morpheme can end with a consonant".
There are a number of paraphrases like "you have to get the right output no matter what input you assume", but that is not literally true. Example, to get [dɔg] in English, you cannot assume /kæt/. It is also true that the system must compute some output for any input, thus if we knew what the constraints and rankings are in English, we could know what the output is for /ndɔgŋ/.
RotB is also tied to the concept of phonotactics, that is, the purported surface regularities of a language, so if we grant that "mshort" is not a possible word of English, the claim (an independent claim) is that you have to grammatically guarantee that fact. Since no input can map /XYZ/ to "mshort" and you cannot prohibit underlying /XYZ/, then the system of constraint have to always remove "mshort" from the surface. A possible phonotactic generalization about English is that nasal plus fricative sequences are not allowed syllable-initially. Therefore some arrangement of constraints must always filter out such clusters, although we do not know if that happens by deleting the nasal, the fricative, inserting a vowel or swapping the consonants. It is unclear what constitutes a mandatorily-encoded phonotactic pattern in OT, for example is it a phonotactic pattern that [blɪnd, blʊnd, plɪnd, plʊnd] are not words of English? If there is some such constraint, then RotB says that there could be such word, which is changed in some way to an existing word.