What wire size do I need for a 200A residential service?
If the load is feeding the entire home it can be de rated to 83% as long as the calculated load Is below this 166A  310.15.B.7.1 (&amp; .2)
AND
The ampacity of the feeder can not be below 83% so 4/0 rated at 180 amps is the minimum
The 75 degree table is used. Per NEC 110.14.C.1.b
@Jack had it I provided the code references.
Yes if overhead run some think that table can be used but only if the feed has less than 24” of conduit.