D-Dimensional hypercubes and the Euler and MacNeish conjectures

charles F. Laywine, Gary L. Mullen, Geoff Whittle

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We give a construction for large sets of mutually orthogonal hypercubes of dimensional d given sets of mutually orthogonal latin squares and hypercubes of lower dimension. We also consider d>-2 dimensional versions of the Euler and MacNeish conjectures as well as discussing applications to improved constructions of (t, m, s)-nets, useful in pseudorandom number generation and quasi-Monte-Carlo methods of numerical integration.

Original languageEnglish (US)
Pages (from-to)223-238
Number of pages16
JournalMonatshefte für Mathematik
Issue number3
StatePublished - Sep 1995

All Science Journal Classification (ASJC) codes

  • General Mathematics


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