Open Access
December, 1955 Further Remark on the Maximum Number of Constraints of an Orthogonal Array
Esther Seiden
Ann. Math. Statist. 26(4): 759-763 (December, 1955). DOI: 10.1214/aoms/1177728434


R. C. Bose and K. A. Bush [1] showed how to make use of the maximum number of points, no three collinear, in finite projective spaces for the construction of orthogonal arrays. In particular, this enabled them to construct an orthogonal array (81, 10, 3, 3). They proved, on the other hand, that in the case considered the maximum number of constraints does not exceed 12. Hence they state, "We do not know whether we can get 11 or 12 constraints in any other way." A partial solution to this problem was given by the author [2]. It was shown that the number of constraints cannot exceed 11. The purpose of this paper is to give a complete solution to the above stated problem, namely, to prove that no way exists which could give a number of constraints, of the considered orthogonal array, greater than ten. As a consequence of the proof it follows also that any orthogonal array with ten constraints satisfies a unique algebraic solution. It is not known, however, whether the arrays constructed by the geometrical method form the totality of orthogonal arrays of the considered type.


Download Citation

Esther Seiden. "Further Remark on the Maximum Number of Constraints of an Orthogonal Array." Ann. Math. Statist. 26 (4) 759 - 763, December, 1955.


Published: December, 1955
First available in Project Euclid: 28 April 2007

zbMATH: 0065.24514
MathSciNet: MR74357
Digital Object Identifier: 10.1214/aoms/1177728434

Rights: Copyright © 1955 Institute of Mathematical Statistics

Vol.26 • No. 4 • December, 1955
Back to Top