Geodesic
Recursive Methods for Construction of Balanced N-ary Block Designs
Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 189-200.

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This paper presents a recursive method for the construction of balanced n-ary block designs. This method is based on the analogy between a balanced incomplete binary block design (B.I .E .B) and the set of all distinct linear sub-varieties of the same dimension extracted from a finite projective geometry. If V1 is the first B.I .E .B resulting from this projective geometry, then by regarding any block of V1 as a projective geometry, we obtain another system of B.I .E .B. Then, by reproducing this operation a finite number of times, we get a family of blocks made up of all obtained B.I .E .B blocks. The family being partially ordered, we can obtain an n-ary design in which the blocks are consisted by the juxtaposition of all binary blocks completely nested. These n-ary designs are balanced and have well defined parameters. Moreover, a particular balanced n-ary class is deduced with an appreciable reduction of the number of blocks.
Keywords: Balanced Incomplete Binary Blocks, N-ary Designs, Finite Projective Geometry, Finite Linear Sub-Variety 
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Gheribi-Aoulmi, Z.; Bousseboua, M. Recursive Methods for Construction of Balanced N-ary Block Designs. Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 189-200. http://geodesic.mathdoc.fr/item/SMJ2_2005_31_3_a1/