Existence results for doubly near resolvable (υ, 3, 2)-BIBDs

✍ Scribed by E.R. Lamken; S.A. Vanstone

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 788 KB
• Volume: 120
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90571-a

✦ Synopsis

Let V be a set of u elements. A (1,2; 3,v, I)-frame F is a square array of side v which satisfies the following properties. We index the rows and columns of F with the elements of V, V= {x Ir x2,, ,x,}.

(1) Each cell is either empty or contains a 3-subset of V. (2) Cell (xi. xi) is empty for i= 1,2, . , u.

(3) Row xi of F contains each element of V-{xi} once and column xi of F contains each element of V-{xi} once. (4) The collection of blocks obtained from the nonempty cells of F is a (u, 3,2)-BIBD.

A (1,2; 3, v, I)-frame is a doubly near resolvable (v,3,2)-BIBD. In this paper, we first present a survey of existence results on doubly near resolvable (v, 3,2)-BIBDs and (1,2; 3, a, I)-frames. We then use frame constructions to provide a new infinite class of doubly near resolvable (v,3,2)-BIBDs by constructing

(1,2,3,u, I)-frames.