Spencer Discrepancy Constant

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 …

Covering-code reformulation: only n = 12, 15, 18, 20 can beat 7/sqrt(17), the record is Ostergard-Kaikkonen K(17,5) <= 32, and exhaustive negatives

**Reformulation.** Write each row of A as a binary word. For a sign vector x, |<a_i, x>| >= d holds iff x is within Hamming distance R = (n - d)/2 of a_i or of its complement. Hence > disc(A) >= d i…