Abstract
SUMMARY Methods for constructing non-directional balanced polycross designs are presented, the balance being over row, column, and diagonal neighbours. The idea of a terrace is generalised and used to construct a set of arrays which enjoys complete balance. The arrays are then combined to obtain smaller, balanced designs; explicit constructions are given for ν < 20 varieties. Many of the designs are in v or v + 1 replicates and have treatments balanced in rows and columns. As an additional benefit, some of the EBIBD designs of Kiefer and Wynn (1981) are produced.
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