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Biometrika 1976 63(1):83-92; doi:10.1093/biomet/63.1.83
© 1976 by Biometrika Trust
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A new class of resolvable incomplete block designs

H. D. PATTERSON and E. R. WILLIAMS

Agricultural Research Council Unit of Statistics, University of Edinburgh
Department of Statistics, University of Edinburgh

This paper describes an algorithm for constructing resolvable incomplete block designs for any number of varieties v and block size k such that v is a multiple of k. These designs are called {alpha}-designs. They include as special cases some lattice and resolvable cyclic designs. Additional designs with two block sizes differing by one plot are derived by omitting one or more varieties of the {alpha}-designs. The designs are shown to be available with high efficiency factors for a wide range of parameter values.

Key Words: Concurrence matrix • Cyclic design • Efficiency factor • Incomplete block design • Rectangular lattice • Resolvability • Square lattice • Variety trial


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