Two incomplete block designs, the lattice and triple lattice, are discussed. Their construction, the field plans, experimental results, the statistical analysis and new features of the mathematical theory are included.

The two experiments consist of yield tests of 81 double-crosses of corn. They are used to illustrate a new method of analysis in which the inter-block information is recovered. The analysis is presented in such a way that it can be adopted as the standard method of analyzing lattice and triple lattice experiments.

The recovery of inter-block information and the reduction of block size from 81 to 9 plots per block resulted in a notable increase in precision when compared with the randomized complete block designs. The gain was 85 percent for the lattice experiment and 73 percent for the triple lattice experiment.