Abstract
Here, two three-class association schemes called tetrahedral association scheme and cubical association scheme have been proposed along with methods of constructing partially balanced incomplete block designs based on these schemes. Designs based on cubical association scheme are found to be resolvable. An outline of the method of analysis of the designs has also been presented together with a list of PBIB(3) designs obtained using the proposed methods for number of treatments v < 100. The proposed designs are seen to be more efficient than the circular lattices [PBIB(3) designs] with the same number of experimental units for the estimation of elementary treatment effect contrasts.