Abstract
A balanced n-ary design is a design on V elements arranged in B blocks of size K such that each element can occur 0,1,2,..., or n-1 times in each block (so that the blocks are collections of elements rather than subsets) and such that
, constant, where nij is the number of times the ith element occurs in the jth block, i=1, ...,V, j=1,...,B. So a balanced binary design is merely a balanced incomplete block design (BIBD).
Any m BIBDs, based on the same set of elements, are used in two constructions to yield balanced (m+1)-ary designs. Some interesting combinatorial identities are involved.
Similar constructions using BIBDs with λ=1 and 2 yield other BIBDs.
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© 1979 Springer-Verlag
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Morgan, E.J. (1979). Construction of balanced designs and related identities. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102686
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DOI: https://doi.org/10.1007/BFb0102686
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