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December, 1960 Third Order Rotatable Designs in Three Dimensions
Norman R. Draper
Ann. Math. Statist. 31(4): 865-874 (December, 1960). DOI: 10.1214/aoms/1177705662


Two recent papers by Bose and Draper [1] and Draper [3] showed how it was possible, by combining certain sets of points, to construct infinite classes of second order rotatable designs in three and more dimensions. In this paper, third order rotatable designs in three dimensions are discussed. First, a general theorem is proved that provides the conditions under which a third order rotatable arrangement of points in $k$ dimensions is non-singular. The four previously known third order designs in three dimensions are stated; it is then shown how some of the second order design classes constructed earlier [1] may be combined in pairs to give infinite classes of sequential third order rotatable designs in three dimensions. One example of such a combination is worked out in full and it is shown that two of the four known designs are special cases of this class. A summary of further third order rotatable design classes that have been shown to exist, and that have been tabulated by the author, concludes the paper.


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Norman R. Draper. "Third Order Rotatable Designs in Three Dimensions." Ann. Math. Statist. 31 (4) 865 - 874, December, 1960.


Published: December, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0103.12004
MathSciNet: MR119335
Digital Object Identifier: 10.1214/aoms/1177705662

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 4 • December, 1960
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