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May, 1975 Further Contributions to the Theory of $F$-Squares Design
A. Hedayat, D. Raghavarao, E. Seiden
Ann. Statist. 3(3): 712-716 (May, 1975). DOI: 10.1214/aos/1176343134


The main purpose of this paper is four-fold. First, to prove that the best upper bound on the number of mutually orthogonal $F(n, \lambda)$ squares is $(n - 1)^2/(m - 1)$, where $m = n/\lambda$. Second, to show that this upper bound is achievable if $m$ is a prime or prime power and $\lambda = m^h$. Third, to present a set of four mutually orthogonal $F(6; 2)$ squares design. This latter design is important because there are no orthogonal Latin squares of order 6 which could be used for this purpose. Fourth, to indicate a method of composing orthogonal $F$-squares designs. In addition, we have pointed out the way one may construct orthogonal fractional factorial designs and orthogonal arrays from these designs.


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A. Hedayat. D. Raghavarao. E. Seiden. "Further Contributions to the Theory of $F$-Squares Design." Ann. Statist. 3 (3) 712 - 716, May, 1975.


Published: May, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0304.62010
MathSciNet: MR396297
Digital Object Identifier: 10.1214/aos/1176343134

Primary: 62K10
Secondary: 05B15 , 62K15

Keywords: $F$-square design , Latin squares , orthogonal arrays , orthogonal fractional factorial

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 3 • May, 1975
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