Truncated triangular association scheme and related partial diallel crosses

Abstract

A new association scheme called truncated triangular (TT) with five associate classes when v = p(p-2)/2 with p an even positive integer ≥ 8, has been discussed and used to construct partial diallel crosses (PDC). The analysis of the design is based on the characteristic roots and idempotent matrices of the matrix A = NN' where N is the incidence matrix of the design. Of the three designs for PDC constructed with the help of TT association scheme, Design I is found to be consistently more efficient than the other two.