\log N)^{d/2}/N$
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Infinite sequences with optimal diaphony, periodic $L_2$-discrepancy, and beyond
arXiv:2606.05482v1 Announce Type: new Abstract: We investigate the periodic $L_2$-discrepancy of infinite sequences $\S_d$ in $[0,1)^d$ and its analytic counterpart, the diaphony. We prove that infinite order-2 digital sequences over $\mathbb{F}_2$ attain the optimal order $L_{2,N}^{{\rm per}}(\S_d) \le C_d (\log N)^{d/2}/N$ for all $N \in \mathbb{N}\setminus \{1\}$, matching known lower bounds for infinitely many $N \in \mathbb{N}$.
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