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September, 1956 A Method of Constructing Partially Balanced Incomplete Block Designs
J. W. Archbold, N. L. Johnson
Ann. Math. Statist. 27(3): 624-632 (September, 1956). DOI: 10.1214/aoms/1177728172


Partially balanced incomplete block designs were introduced by Bose and Nair [1], who described a number of methods of constructing such designs. Among these methods there is one based on incidence properties of finite geometries. This uses the finite geometries associated with the Galois field $GF(p^n)$ with addition and multiplication $(\operatorname{mod} p$). By weakening the geometrical structure (or, equivalently, by weakening the rules of addition and multiplication), it is possible to obtain new designs. A basic feature of a finite projective geometry is that the coordinates are elements of a finite field. What we do here is to allow the coordinates to belong instead to a linear associative algebra $\mathscr{a},$ of finite order $n$ and with modulus, over a finite field $F.$ The procedure is summarized below and explained with more detail in regard to two designs. (For accounts of a similar geometrical theory, using an infinite field, see [7], [8], [9].)


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J. W. Archbold. N. L. Johnson. "A Method of Constructing Partially Balanced Incomplete Block Designs." Ann. Math. Statist. 27 (3) 624 - 632, September, 1956.


Published: September, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0072.36605
MathSciNet: MR80426
Digital Object Identifier: 10.1214/aoms/1177728172

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 3 • September, 1956
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