# Recursive Methods for Construction of Balanced N-ary Block Designs

Gheribi-Aoulmi, Z.; Bousseboua, M.

Serdica Mathematical Journal (2005)

- Volume: 31, Issue: 3, page 189-200
- ISSN: 1310-6600

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topGheribi-Aoulmi, Z., and Bousseboua, M.. "Recursive Methods for Construction of Balanced N-ary Block Designs." Serdica Mathematical Journal 31.3 (2005): 189-200. <http://eudml.org/doc/219563>.

@article{Gheribi2005,

abstract = {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.},

author = {Gheribi-Aoulmi, Z., Bousseboua, M.},

journal = {Serdica Mathematical Journal},

keywords = {Balanced Incomplete Binary Blocks; N-ary Designs; Finite Projective Geometry; Finite Linear Sub-Variety; finite projective geometries},

language = {eng},

number = {3},

pages = {189-200},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Recursive Methods for Construction of Balanced N-ary Block Designs},

url = {http://eudml.org/doc/219563},

volume = {31},

year = {2005},

}

TY - JOUR

AU - Gheribi-Aoulmi, Z.

AU - Bousseboua, M.

TI - Recursive Methods for Construction of Balanced N-ary Block Designs

JO - Serdica Mathematical Journal

PY - 2005

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 31

IS - 3

SP - 189

EP - 200

AB - 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.

LA - eng

KW - Balanced Incomplete Binary Blocks; N-ary Designs; Finite Projective Geometry; Finite Linear Sub-Variety; finite projective geometries

UR - http://eudml.org/doc/219563

ER -

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