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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.
The object of this paper is the construction of balanced incomplete block designs with k = 7. This paper continues the work begun by Hanani, who solved the construction problem for designs with a block size of 7, and with λ = 6, 7, 21 and 42. The construction problem is solved here for designs with λ > 2 except for v = 253, λ = 4, 5; also for λ = 2, the(More)