On functional successive minima

In the classical Geometry of Numbers, the calculation of successive minima may be quite difficult, even in using the norm coming from a distance function associated to a set. In the literature, there seem to be hardly any analogues when is replaced by the algebraic closure of a function field in one variable and one uses a norm arising from the absolute height. Here, we calculate a one-parameter family of examples that naturally arose in our recent paper on bounded heights. We also comment on whether the minima are attained.