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L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets

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 نشر من قبل Lev Markhasin
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English
 تأليف Lev Markhasin




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Dick proved that all order $2$ digital nets satisfy optimal upper bounds of the $L_2$-discrepancy. We give an alternative proof for this fact using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds of the $S_{p,q}^r B$-discrepancy for a certain parameter range and enlarge that range for order $2$ digitals nets. $L_p$-, $S_{p,q}^r F$- and $S_p^r H$-discrepancy is considered as well.



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