We consider designs in linear blocks with border plots, in which a tre
atment may affect the response on the two adjacent plots. Three series
of designs are given: (i) neighbour-balanced designs in complete bloc
ks; (ii) neighbour-balanced designs in blocks each of which lacks one
treatment; (iii) partially neighbour-balanced designs in few complete
blocks. Complete methods of construction and randomization are given.
Optimality properties are discussed.