A construction of -sequences with finite-row generating matrices using global function fields

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• 作者：Roswitha Hofer^a ; ^{roswitha.hofer@jku.at} ; Harald Niederreiter^b ; ^c ; ^{ghnied@gmail.com}
• 关键词：11K31 ; 11K38 ; 11K45 ; 14G15 ; 65C05
• 刊名：Finite Fields and Their Applications
• 出版年：2013
• 出版时间：May, 2013
• 年：2013
• 卷：21
• 期：Complete
• 页码：97-110
• 全文大小：237 K

文摘

For any prime power q and any dimension , we present a construction of -sequences in base q with finite-row generating matrices such that, for fixed q, the quality parameter t is asymptotically optimal as a function of s as . This is the first construction of -sequences that yields finite-row generating matrices and asymptotically optimal quality parameters at the same time. The construction is based on global function fields. We put the construction into the framework of -sequences that was recently introduced by Tezuka. In this way we obtain in many cases better discrepancy bounds for the constructed sequences than by previous methods for bounding the discrepancy.