The paper proves bs(k) ≤ g(k)+2 for k-uniform hypergraphs, determines bs(k)=3 for 3≤k≤13, and improves the known upper bound from k+1 to O(k^{0.525}).
Intersections of random hypergraphs and tournaments.European Journal of Combinatorics, 44:125–139, 2015
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Relative discrepancy of hypergraphs
The paper proves bs(k) ≤ g(k)+2 for k-uniform hypergraphs, determines bs(k)=3 for 3≤k≤13, and improves the known upper bound from k+1 to O(k^{0.525}).