  Sidon sets are those sets such that the sums of two of its elements never
coincide. They go back to the 30s when Sidon asked for the maximal size of a
subset of consecutive integers with that property. This question is now
answered in a satisfactory way. Their natural generalization, called B 2 [g]
sets and defined by the fact that there are at most g ways (up to reordering
the summands) to represent a given integer as a sum of two elements of the set,
are much more difficult to handle and not as well understood. In this article,
using a numerical approach, we improve the best upper estimates on the size of
a B 2 [g] set in an interval of integers in the cases g = 2, 3, 4 and 5.
