Let F be the hyperelliptic genus 2 field given by
y^2 + x*y + x^5 + x^3 + x^2 + x.
Using the notation of Magma, let D be the divisor
(x^3 + x + 1) + (x^2 + x + 1, y + x + 1) +
+(x^2 + x + 1, y + 1)
(The first of the places in the support of D has degree 6, the other two has degree 2.)
Let S be the set of rational places in F.
Then F^D_S, the largest abelian extension of F with conductor <=D such that all places in S split completely, has genus 46 and 36 rational places. This can easily be verified using Magma.