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CodingTheoretic Constructions for (t, m, s)Nets and Ordered Orthogonal Arrays
, 2002
"... Introduction (t; m; s)\Gammanets were defined by Niederreiter [17] in the context of quasiMonte Carlo methods of numerical integration. Niederreiter pointed out close connections to certain combinatorial and algebraic structures. This was made precise in the work of Lawrence, Mullen and Schmid [11 ..."
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Introduction (t; m; s)\Gammanets were defined by Niederreiter [17] in the context of quasiMonte Carlo methods of numerical integration. Niederreiter pointed out close connections to certain combinatorial and algebraic structures. This was made precise in the work of Lawrence, Mullen and Schmid [11, 15, 24]. These Research partially supported by the Austrian Science Fund (FWF) Grant S8311MAT. authors introduce a large class of finite combinatorial structures, which we will call ordered orthogonal arrays OOA. These OOA contain orthogonal arrays as a subclass. (t; m; s) q nets (that is, (t; m; s)nets in base q as in the original Definition 2.2 in [17]) are equivalent to another parametric subclass of OOA. Loosely speaking a (t; m; s) q net is linear if it is defined over the field IF q with q elements. The duality between linear codes and linear orthogonal arrays carries over to the more general setting of linear OOA (see [14] or [20]). Here OOA generalize orthogonal arrays (dual