Enumeration of balanced ternary designs

✍ Scribed by Petteri Kaski; Patric R.J Östergård

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 206 KB
• Volume: 138
• Category: Article
• ISSN: 0166-218X
• DOI: 10.1016/s0166-218x(03)00276-2

✦ Synopsis

A (V; B; 1; 2; R; K; ) balanced ternary design is a pair (V; B), where V is a V -set of points and B is a collection of B K-multisubsets of V called blocks, such that each point appears R times in the blocks and no block contains a point with multiplicity greater than two. Each point must appear in 1 blocks with multiplicity one and in 2 blocks with multiplicity two. Additionally, every pair of distinct points must appear exactly times in the blocks of the design. A backtrack search algorithm with isomorph rejection is described and employed to enumerate the balanced ternary designs with V 6 10, B 6 30, and R 6 15 for all but 12 of the 155 possible design classes with these parameters.