Coexistence of some B.I.B. Designs

Constructions of nested directed BIB designs

A directed BIB design DB(k, A; v) is a BIB design B(k, 2A; v) in which the blocks are transitively ordered k-tuples and each ordered pair of elements occurs in exactly A blocks. A nested directed BIB design NDB(k, A; v) of form IT2<n<k-l(njn, An)in is a DB(k, A; v) where each block contains E2<n<k-l injn mutually disjoint subblocks, injn subblocks of which are partitIoned into in mutually disjo...

Notes on the structure of support in BIB designs

A note on BIB designs with nested rows and columns

In [1] Aggarwal & Arasu devised a construction for balanced incomplete block designs having nested rows and columns. Their construction uses finite fields and depends on the existence of primitive elements having certain properties. They conjectured that such primitive elements always exist. The purpose of this short note is to point out that their conjecture is true. The purpose of ~his note i...

Pairwise additive 1-rotational BIB designs with λ=1

The existence of pairwise additive balanced incomplete block (BIB) designs and pairwise additive cyclic BIB designs with λ = 1 has been discussed through direct and recursive constructions in the literature. This paper takes BIB designs with 1-rotational automorphisms and then the existence of pairwise additive 1-rotational BIB designs is investigated for λ = 1. Finally, it is shown that there ...

Remarks on Bib Designs with Repeated Blocks By