EFFICIENT BLOCK-DESIGNS FOR SETTINGS WITH SPATIALLY CORRELATED ERRORS

Two-dimensional block designs, with block size p x 2 for nu treatments , are studied for situations in which the errors are spatially correla ted. Conditions for universal optimality are given for two different e rror covariance structures, the doubly geometric, for which the correl ations decay rapidly, and the autonormal, which exhibits a slower rate of decay. In the special cases of p=1/2 nu for even nu to obtain comp lete blocks, and p=1/2(v-1) for odd nu for nearly complete blocks, num erical calculations establish that much smaller designs, using only a fraction of the blocks required by universal optimality, are also reas onably efficient. A table of designs with nu less than or equal to 30 is included.