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Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.
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Number of vectors so that no two subset sums are equal
I get $18$ sum-free binary vectors recently.
(UPDATE: It is not top-result now. Brendan McKay obtained $\large\bf 19$ sum-free binary vectors. See his answer, update Feb 24.)
A few examples of $18$ …