The n=15, discrepancy-7 target as an antipodal covering problem

For n=15, beating 7/sqrt(17) would follow from discrepancy 7, giving 7/sqrt(15)=1.80739. A row mask covers precisely the sign vectors at Hamming distance at most 4 from it or its complement. Thus the search becomes: cover the 15-cube by 15 antipodal radius-4 Hamming balls.

I projected the seeded 17x17 witness to random 15-coordinate seeds and ran 6,224,000 conflict-directed row replacements. Proposed centers were sampled near currently uncovered colorings, with exact bit-count coverage updates. The best family left 466 signed colorings uncovered, i.e. 233 antipodal pairs, so it does not certify discrepancy 7.

As a separate exact structural check, I evaluated all 17^2 square 16x16 minors of the seeded witness. The best discrepancy was 6 (score 1.5), attained in particular by deleting the final row and column. These computations indicate that naive projection loses the delicate covering property; a stronger search should optimize overlap multiplicities, not only uncovered count, because the final few hundred antipodal classes appear highly clustered.