Resolvable balanced incomplete block designs with subdesigns of block size 4

Resolvable balanced incomplete block designs with subdesigns of block size 4

In this paper, we look at resolvable balanced incomplete block designs on v points having blocks of size 4, briefly (v, 4, 1) RBIBDs. The problem we investigate is the existence of (v, 4, 1) RBIBDs containing a (w, 4, 1) RBIBD as a subdesign. We also require that each parallel class of the subdesign should be in a single parallel class of the containing design. Removing the subdesign gives an i...

Super-Simple Resolvable Balanced Incomplete Block Designs with Block Size 4 and Index 4

The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007

Balanced incomplete block designs with block size~9: Part III

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.

Super-simple balanced incomplete block designs with block size 4 and index 5

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v, 4, λ)-BIBDs have been determined for λ = 2, 3, 4 and 6. When λ = 5, the necessary conditions of such a d...

Splitting balanced incomplete block designs