Recursive Methods for Construction of Balanced N-ary Block Designs


Autoria(s): Gheribi-Aoulmi, Z.; Bousseboua, M.
Data(s)

18/06/2012

18/06/2012

2005

Resumo

2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10.

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.

Identificador

Serdica Mathematical Journal, Vol. 31, No 3, (2005), 189p-200p

1310-6600

http://hdl.handle.net/10525/1764

Idioma(s)

en

Publicador

Institute of Mathematics and Informatics Bulgarian Academy of Sciences

Palavras-Chave #Balanced Incomplete Binary Blocks #N-ary Designs #Finite Projective Geometry #Finite Linear Sub-Variety
Tipo

Article