A ground rod never needs more than a #6. 250.66(A) You size your other electrodes by T250.66 which has to do with the size of the service conducts. Look at Notes 1 and 2
250.52(A)(5) requires ground rods to be a minimum diameter of 5/8" and a length of 8' regardless of the service size. Listed ground rods can be smaller in diameter.