Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes
In [Monatsh. Math. 104, 273-337 (1987; Zbl 0626.10045)], the author introduced and gave various constructions for and properties of \((t,m,s)\)-nets. Such nets are of importance in the study of low-discrepancy point sets in \([0,1)^s, s\geq 2.\) Such nets were shown to be related to various combinatorial structures, for example to sets of mutually orthogonal latin squares. \textit{G. L. Mullen} and \textit{G. Whittle} [Monatsh. Math. 113, 265-273 (1972; Zbl 0765.11032)], extended this equivalence via sets of orthogonal hypercubes of higher dimensions. In this note the author shows the equivalence of certain \((t,m,s)\)-nets to orthogonal arrays. He also discusses a combinatorial problem for vector spaces over finite fields which generalizes a problem from algebraic coding theory, namely that of determining the largest minimum distance which can be achieved by a linear code over a finite field with given length and dimension.
scientific article; zbMATH DE number 94543
scientific article