Most digits with all pairwise sums different

An integer has the property that adding any two of its digits (taken from different positions) never gives the same total twice; for instance $174$ works because $1+7$, $1+4$ and $7+4$ are all different. What is the greatest number of digits such an integer can have?

5. Digits must be distinct (a repeated digit plus any third digit gives a repeated sum), so we need a set of digits from $0$ to $9$ with all pairwise sums distinct. $\{0,1,2,4,7\}$ works (e.g. $74210$), and a check of all six-element subsets shows none does, since six digits would need $15$ distinct sums.