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We are interested in point sets with very low star discrepancy. This means that we aim on finding point sets \(\mathcal {P}\) for which the absolute local discrepancy, \( |\Delta _{\mathcal {P},N}(\boldsymbol{y})| =\left| \frac{A([\textbf{0},\boldsymbol{y}),\mathcal {P},N)}{N}-\lambda _s([\textbf{0},\boldsymbol{y}))\right| , \) is as small as possible for all \(\boldsymbol{y}\in (0,1]^s\) . Our strategy for achieving this goal is to discretize the problem and to investigate point sets \(\mathcal {P}\) .

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(t, m, s)-Nets and (t, s)-Sequences

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  • 发表日期：

    2026年

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  • Gunther Leobacher,
  • Friedrich Pillichshammer

摘要

We are interested in point sets with very low star discrepancy. This means that we aim on finding point sets \(\mathcal {P}\) for which the absolute local discrepancy, \( |\Delta _{\mathcal {P},N}(\boldsymbol{y})| =\left| \frac{A([\textbf{0},\boldsymbol{y}),\mathcal {P},N)}{N}-\lambda _s([\textbf{0},\boldsymbol{y}))\right| , \) is as small as possible for all \(\boldsymbol{y}\in (0,1]^s\) . Our strategy for achieving this goal is to discretize the problem and to investigate point sets \(\mathcal {P}\) .