Summary An example of data for which the power family transformation does not produce satisfactory distributional properties is discussed, and an alternative one‐parameter family of transformations is suggested. In this example, the unsatisfactory feature of the power transformation was its failure to deal with a symmetric distribution with long tails.

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Resolvable row-column designs are widely used in field trials to control variation and improve the precision of treatment comparisons. Further gains can often be made by using a spatial model or a combination of spatial and incomplete blocking components. Martin, Eccleston, and Gleeson presented some general principles for the construction of robust spatial block designs which were addressed by spatial designs based on the linear variance (LV) model. In this article we define the two-dimensional form of the LV model and investigate extensions of the Martin et al. principles for the construction of resolvable spatial row-column designs. The computer construction of efficient spatial designs is discussed and some comparisons made with designs constructed assuming an autoregressive variance structure.

Summary The class of regular graph (RG) designs, conjectured to be optimal among all incomplete block designs, is defined. The results of a systematic search of the class of RG designs are given for all cases in which v ≤ 12, r ≤ 10 and v ≤ b. In nearly every case, the optimum design is determined for each of the three optimality criteria: A, D and E. For v > b, we present the duals of the optimal designs for v < b. Many of the designs are new and these are tabulated in a back‐up report.