How to find a set $A \subset \mathbb{N}$ such that any sum of at most three Elements $a_i \in A$ is different if at least one element in the sum is different.

**Example with $|A|=3$:** Out of the set $A := \{1,7,11\}$ follow 19 sums 1,2,3,7,8,9,11,12,13,14,15,18,19,21,22,23,25,29,33 which are all distinct!

Is there an algorithm to construct such sets for a given number of elements $n=|A|$ with the smallest maximum possible?