count has 19 distinct synonyms spread across 7 of its 12 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.
name or recite the numbers in ascending order
“The toddler could count to 100”
include as if by counting
“I can count my colleagues in the opposition”
have a certain value or carry a certain weight
“each answer counts as three points”
the total number counted
“a blood count”
the act of counting; reciting numbers in ascending order
“the counting continued for several hours”
a nobleman (in various countries) having rank equal to a British earl
Synonyms, antonyms and the broader and narrower relations for count come from Princeton University’s WordNet. Full sources and licences.