A symmetrized lattice of 2n points in terms of an irrational real number α is considered in the unit square, as in the theorem of Davenport. If α is a quadratic irrational, the square of the 80fad2e077594a688a241" title="Click to view the MathML source">L2 discrepancy is found to be e7d7e0" title="Click to view the MathML source">c(α)logn+O(loglogn) for a computable positive constant a2" title="Click to view the MathML source">c(α). For the golden ratio φ , the value 8e36bf4ad18898a70cdd6"> yields the smallest 80fad2e077594a688a241" title="Click to view the MathML source">L2 discrepancy of any sequence of explicitly constructed finite point sets in the unit square. If the partial quotients e871ef59796745910b1b41215453eb2e" title="Click to view the MathML source">ak of α grow at most polynomially fast, the 80fad2e077594a688a241" title="Click to view the MathML source">L2 discrepancy is found in terms of e871ef59796745910b1b41215453eb2e" title="Click to view the MathML source">ak up to an explicitly bounded error term. It is also shown that certain generalized Dedekind sums can be approximated using the same methods. For a special generalized Dedekind sum with arguments a, b an asymptotic formula in terms of the partial quotients of 83de3cc77dfa3d613c13e8422b81e01c"> is proved.