The article I have checked for Baker's theorem is [Waldschmidt's](http://www.math.jussieu.fr/~miw/articles/pdf/GDL/SemBxMSGB.pdf). But the article and the citations therein are from the time of '88. Question:

> What is the the strongest known lower bound for Baker's theorem on linear forms on logarithms?

Similarly for p-adic Baker.