mat has 20 distinct synonyms spread across 8 of its 11 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a thick flat pad used as a floor covering
sports equipment consisting of a piece of thick padding on the floor for gymnastic sports
a mass that is densely tangled or interwoven
“a mat of weeds and grass”
the property of having little or no contrast; lacking highlights or gloss
a foundation (usually on soft ground) consisting of an extended layer of reinforced concrete
Synonyms, antonyms and the broader and narrower relations for mat come from Princeton University’s WordNet. Full sources and licences.