Soit une suite de Halton á s dimensions. Soit la discrépance de la suite . Il est connu que lorsque . Dans cet article, nous montrons que cette estimation est exacte :
Let be an s-dimensional Halton's sequence. Let be the discrepancy of the sequence . It is known that as . In this paper, we prove that this estimate is exact:
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@article{CRMATH_2016__354_5_445_0, author = {Levin, Mordechay B.}, title = {On the lower bound of the discrepancy of {Halton's} sequence {I}}, journal = {Comptes Rendus. Math\'ematique}, pages = {445--448}, publisher = {Elsevier}, volume = {354}, number = {5}, year = {2016}, doi = {10.1016/j.crma.2016.02.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2016.02.003/} }
TY - JOUR AU - Levin, Mordechay B. TI - On the lower bound of the discrepancy of Halton's sequence I JO - Comptes Rendus. Mathématique PY - 2016 SP - 445 EP - 448 VL - 354 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2016.02.003/ DO - 10.1016/j.crma.2016.02.003 LA - en ID - CRMATH_2016__354_5_445_0 ER -
%0 Journal Article %A Levin, Mordechay B. %T On the lower bound of the discrepancy of Halton's sequence I %J Comptes Rendus. Mathématique %D 2016 %P 445-448 %V 354 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2016.02.003/ %R 10.1016/j.crma.2016.02.003 %G en %F CRMATH_2016__354_5_445_0
Levin, Mordechay B. On the lower bound of the discrepancy of Halton's sequence I. Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 445-448. doi : 10.1016/j.crma.2016.02.003. http://archive.numdam.org/articles/10.1016/j.crma.2016.02.003/
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