Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 31, No 3, (2005), 189p-200p
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
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.