Point sets with uniformity properties and orthogonal hypercubes

G. L. Mullen, G. Whittle

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

The theory of (t, m, s)-nets is useful in the study of sets of points in the unit cube with small discrepancy. It is known that the existence of a (0, 2, s)-net in base b is equivalent to the existence of s-2 mutually orthogonal latin squares of order b. In this paper we generalize this equivalence by showing that for t≥0 the existence of a (t, t+2, s)-net in base b is equivalent to the existence of s mutually orthogonal hypercubes of dimension t+2 and order b. Using the theory of hypercubes we obtain upper bounds on s for the existence of such nets. For b a prime power these bounds are best possible. We also state several open problems.

Original languageEnglish (US)
Pages (from-to)265-273
Number of pages9
JournalMonatshefte für Mathematik
Volume113
Issue number4
DOIs
StatePublished - Dec 1 1992

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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