Generally speed doesn't effect latency unless you run out of bandwidth.
What really matter is distance from the server, the close you are the lower the pings.
Line quality can also effect latency, poor line quality could lead to packet loss which will effect latency.
Both down and upload speeds are important as you need to send and receive data.
The only other thing that would effect pings with out moving closer to the server would be moving from a copper line to a fibre line and that's only if the server you are playing on is local (same land mass).
Judging by your speeds i'm going to assume you are already using some form of fibre/hybrid line?