Davenport's theorem in the theory of irregularities of point distribution (Q1405638)

The authors study distributions \(\mathcal{D}_N\) of \(N\) points in the unit square \(U^2\) with minimal order of \(L_2\)-discrepancy \(\mathcal{L}_2[\mathcal{D}_N]<C(\log N)^{1/2}\), where the constant \(C\) is independent of \(N\). The approach uses Walsh functions and can be generalized to higher dimensions; see the paper by the authors [J. Reine Angew. Math. 545, 67--95 (2002; Zbl 1083.11049)].