furthest has 5 distinct synonyms spread across 3 of its 3 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.
to the greatest degree or extent or most advanced stage (`furthest' is used more often than `farthest' in this abstract sense)
“went the furthest of all the children in her education”
to the greatest distance in space or time (`farthest' is used more often than `furthest' in this physical sense)
“see who could jump the farthest”
(comparatives of `far') most remote in space or time or order
“had traveled to the farthest frontier”
Synonyms, antonyms and the broader and narrower relations for furthest come from Princeton University’s WordNet. Full sources and licences.