SUMMARY In the early stages of a plant selection program, field experiments are characterized by having many test lines and a limited amount of material available for each line. The present design was proposed to cope with such experimental conditions by using control plots to adjust for environmental heterogeneity. The structure is a split-plot design, where the whole-plots can be laid out in any standard design, but the arrangements of subplots is always 3 x 3 with the centre point used as a control. The shape of subplot needs to be square or nearly square, so that the distances between the centre plot and its corresponding eight test plots are relatively uniform. The control lines are assigned to the control plots according to the design specification for the whole-plots, and the test lines are assigned randomly to the noncontrol plots. The number of control plots under the present design is approximately 13-17% of the total number of plots. The p x p Latin square is used as an example to demonstrate the basic idea of the design. Methods of analysis are also discussed. In plant selection programs, breeders usually start with a large number of test lines which come either from crossing or through introduction from foreign sources. The number of lines can range from several hundred to several thousand. To conduct a field experiment for such a large population is extremely difficult for a number of reasons, among them that environmental heterogeneity in the field cannot be easily taken into account. To complicate the matter further, material available for each test line is often limited, sometimes being sufficient for only one replication. Thus designs for variety trials involving large numbers of test lines, for example, lattice, lattice square and quasifactorial designs, all of which require replication, cannot be used; similarly, designs such as chain blocks (Youden and Connor, 1953; Mandel, 1954), which require that a substantial number of test lines have at least two replications, cannot be applied. To circumvent the difficulties arising from nonreplicated experiments, Federer (1956) proposed a class of design called 'augmented design'. The basic idea is to include control lines for which enough material is available and repeat them several times in a standard design. Each repetition of the control lines is embedded in a block (or incomplete block, or cell, depending on the design used) and the test lines are assigned to plots that are not allocated to controls. Estimation of block effects and plot error is done only with respect to control lines. The estimated block effects are used to adjust the observed values of the test lines and the error is used to test the significance of line differences. In addition to the above, Federer and Raghavarao (1975) proposed a special square design (which we will refer to as the F-R design), generated from the Youden square. In this design the control plots are allocated over a square with a constant number of control plots per row and per column, and row and column effects are orthogonal to control lines. Furthermore, Federer, Nair and Raghavarao