D-Dimensional hypercubes and the Euler and MacNeish conjectures

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

doi:10.1007/BF01293673

D-Dimensional hypercubes and the Euler and MacNeish conjectures

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

Mathematics

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18 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	223-238
Number of pages	16
Journal	Monatshefte für Mathematik
Volume	119
Issue number	3
DOIs	https://doi.org/10.1007/BF01293673
State	Published - Sep 1995

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF01293673

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title = "D-Dimensional hypercubes and the Euler and MacNeish conjectures",

abstract = "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.",

author = "Laywine, {charles F.} and Mullen, {Gary L.} and Geoff Whittle",

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AU - Laywine, charles F.

AU - Mullen, Gary L.

AU - Whittle, Geoff

PY - 1995/9

Y1 - 1995/9

N2 - 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.

AB - 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.

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ER -

D-Dimensional hypercubes and the Euler and MacNeish conjectures

Abstract

All Science Journal Classification (ASJC) codes

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