Recursive Methods for Construction of Balanced N-ary Block Designs
Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 189-200
Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library
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
@article{SMJ2_2005_31_3_a1,
author = {Gheribi-Aoulmi, Z. and Bousseboua, M.},
title = {Recursive {Methods} for {Construction} of {Balanced} {N-ary} {Block} {Designs}},
journal = {Serdica Mathematical Journal},
pages = {189--200},
year = {2005},
volume = {31},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2005_31_3_a1/}
}
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/