BIBD's with block-size seven

Halving block designs with block size four

B) is said to have the Size Four property if the blocks in B can be partitioned into two isomorphic sets. In this paper we construct block with four with the property, thus the exception of 6 A. Rosa [4]).

Some new near resolvable BIBDs with k=7 and resolvable BIBDs with k=5

Frames with Block Size Four

We investigate the spectrum for frames with block size four, and discuss several applications to the construction of other combinatorial designs. Our main result is that a frame of type hu, having blocks of size four, exists if and only if u ≥ 5, h ≡ 0 mod 3 and h(u − 1) ≡ 0 mod 4, except possibly where (i) h = 9 and u ∈ {13, 17, 29, 33, 93, 113, 133, 153, 173, 193}; (ii) h ≡ 0 mod 12 and u ∈ {...

All Directed BIBDs with k = 3 Exist

A directed BIBD with parameters (v,b,r,k,λ*) is a BIBD with parameters (v, b, r, k, 2λ*) in which each ordered pair of varieties occurs together in exactly λ* blocks. It is shown that λ*v(v 1) = 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (v, b, r, k, λ*) BIBD with k = 3. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J and Skill...

Kronecker Products and BIBDs

Recursive constructions are given which permit, under conditions described in the paper, a (v, b, r, k, lambda)configuration to be used to obtain a (v', b', r', k, lambda)-configuration. Although there are many equivalent definitions we will mean by a (v, b, r, k, lambda)-configuration or BIBD that (0, 1)-matrix A of size v x b with row sum r and column sum k satisfying AAT = (r lambda)I + lamb...