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Title: Recursive Methods for Construction of Balanced N-ary Block Designs
Authors: Gheribi-Aoulmi, Z.
Bousseboua, M.
Keywords: Balanced Incomplete Binary Blocks
N-ary Designs
Finite Projective Geometry
Finite Linear Sub-Variety
Issue Date: 2005
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 31, No 3, (2005), 189p-200p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10.
ISSN: 1310-6600
Appears in Collections:Volume 31 Number 3

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