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A range of methods is presented for the recursive construction of sets of orthogonal balanced incomplete block designs. To enable these methods, some new types of designs are deÿned. Some examples of these are given, and pairs of orthogonal BIBDs constructed for k = 3; ; = 2, for all but 12 values of v where v ≡ 0; 1 (mod 3) with v ¿ 6.
We settle all but four of the remaining open small parameter situations for partially balanced incomplete block designs with 2 associate classes (PBIBD(2)) that can be based on Triangular schemes.