Abstract
The diallel cross consists of all possible single crosses among a group of parental lines. Some recent papers have discussed the advantages of performing only a sample of all possible crosses among a large number of parents rather than performing all possible crosses among a smaller number of parents. This recent work is reviewed and two methods of sampling the crosses discussed in considerable detail. These methods lead either to only two different variances for comparing the general combining abilities of the lines or to least square equations for the general combining abilities that are circulant and therefore fairly easy to solve. Numerical values are given to assist in the solution of the least square equations and in assessing the relative efficiencies of the different samples. The estimation of variance components is mentioned.

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