Near-Optimal g-Golomb Rulers

A set of positive integers A is called a
$g$
-Golomb ruler if the difference between two distinct elements of A is repeated up to
$g$
times. This definition is a generalization of the Golomb ruler
$(g = 1)$
. In this paper, we obtain new constructions for
$g$
-Golomb rulers from Golomb rulers, using these constructions we find some suboptimal 2 and 3-Golomb rulers with up to 124 marks and we prove two theorems related to extremal functions associated with this sets improving already known results.