Sentence examples for bib design from inspiring English sources

One may ask whether it is true that a BIB design with the parameters of a residual can be embedded in a symmetric BIB design.

For a proper BIB design, Fisher's inequality b ≥ υ, or equivalently r ≥ k, holds.

A BIB design is said to be symmetric if υ = b, and consequently r = k.

Bhattacharya in 1944, however, gave a counterexample for λ = 3 by exhibiting a BIB design with parameters υ = 16, b = 24, r = 9, k = 6, λ = 3 for which two particular blocks intersect in four treatments and which for that reason cannot be embedded in a symmetric BIB design.

A BIB design is a design with υ treatments and b blocks in which each block is of size k, each treatment is replicated r times, and every pair of distinct treatments occurs together in λ blocks.

A BIB design is said to be resolvable if the set of blocks can be partitioned into subsets, such that the blocks in any subset contain every treatment exactly once.

Methods of constructing BIB designs depend on the use of finite fields, finite geometries, and number theory.

Journal of Statistical Planning and Inference 13, 151 163] obtained a class of balanced incomplete block (BIB) designs β (7, 21, 9, 3, 3), where nine out of ten BIB designs are of repeated blocks.

Ghosh and Shrivastava [Ghosh, D.K., Shrivastava, S.B., 2001. A class of BIB designs with repeated blocks. Journal of Applied Statistics 28, 821 833] obtained another class of BIB designs β (7, 28, 12, 3, 4) with repeated blocks where fourteen out of fifteen BIB designs are of repeated blocks.

In this paper, some constructions of good equidistant codes from balanced arrays and nested BIB designs are described.

In this paper, we will construct some symmetric balanced incomplete block (BIB) designs, group divisible (GD) designs and (r, λ -designs from BCH codes.