D-Dimensional hypercubes and the Euler and MacNeish conjectures |
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| Authors: | charles F Laywine Gary L Mullen Geoff Whittle |
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| Institution: | (1) Department of Mathematics, brock University, L2S 3A1 St. Catharines, Ontario, Canada;(2) Mathematies Department, Victoria University of willington, P. O. Box 600 Wellington, New Zealand;(3) Department of Mathematics, The Pennsylvania State University, 16802 PA, University Park, USA |
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| Abstract: | We give a construction for large sets of mutually orthogonal hypercubes of dimensionald given sets of mutually orthogonal latin squares and hypercubes of lower dimension. We also considerd>-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.This author would like to thank the National Security Agency for partial support under grant agreement # MDA 904-92-H-3044. |
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| Keywords: | Primary 05B15 Secondary 05B30 11K45 |
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