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Digital Sequences with Best Possible Order of L 2 ‐Discrepancy
Author(s) -
Pillichshammer Friedrich
Publication year - 2006
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000073
Subject(s) - mathematics , sequence (biology) , constructive , generator (circuit theory) , order (exchange) , combinatorics , matrix (chemical analysis) , constructive proof , discrete mathematics , pure mathematics , power (physics) , computer science , genetics , physics , materials science , process (computing) , finance , quantum mechanics , economics , composite material , biology , operating system
This paper treats the L 2 ‐discrepancy of digital (0, 1)‐sequences over ℤ 2 , and gives conditions on the generator matrix of such a sequence which guarantee minimal possible order of L 2 ‐discrepancy of the generated sequence. The existence is proved for the first time of digital (0; 1)‐sequences over ℤ 2 with L 2 ‐discrepancy of orderlog N / N . This order is best possible by a result of K. Roth. The existence proof is constructive.
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