  Asymptotically good sequences of ramp secret sharing schemes were given in
[Asymptotically good ramp secret sharing schemes, arXiv:1502.05507] by using
one-point algebraic geometric codes defined from asymptotically good towers of
function fields. Their security is given by the relative generalized Hamming
weights of the corresponding codes. In this paper we demonstrate how to obtain
refined information on the RGHWs when the codimension of the codes is small.
For general codimension, we give an improved estimate for the highest RGHW.
