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For block designs comparing v treatments in b incomplete blocks of size k, consider settings where bk = vr + 1 and $$r(k-1)=\lambda (v-1)$$ r(k-1)=λ(v-1) for integers r and $$\lambda $$ λ . These settings admit designs that possess the symmetry of balanced incomplete block designs and which, though nonbinary, are candidates for optimality in some standard senses. For k = 3, earlier authors have established...
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