A new method of arranging variety trials involving large numbers of varieties is described. This type of arrangement, for which the name pseudo-factorial arrangement is proposed, enables the block size to be kept small without the use of controls.

Various possible types of pseudo-factorial arrangement are discussed in detail and the necessary formulae developed. The appropriate methods of computation are illustrated by numerical examples based on the results of a uniformity trial on orange trees. It is shown that pseudofactorial arrangements are likely to be more efficient than arrangements involving the use of controls. In cases where there is considerable soil heterogeneity they are also markedly more efficient than randomized blocks containing all the varieties. In the chosen example gains in efficiency ranging from 26 to 57 per cent, were obtained.