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4
votes
Size of sets with complete double
Short answer: Such a set $S$ is known as a restricted additive basis.
As observed in comments, the general term to search for is [finite]
additive basis: a finite set $S \subset \mathbb{N}$ such that …
1
vote
$B_k[1]$ sets with smallest possible $m = \max B_k[1]$ for given $k$ and $n = \lvert B_k[1]\...
Since the question asks for exact smallest values, not bounds or asymptotics, it is likely to be a difficult problem.
First note that instead of taking sums of at most $k$ elements, we can take sums o …