A note on 3-blocked designs

✍ Scribed by Luigia Berardi

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 145 KB
• Volume: 5
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/(sici)1520-6610(1997)5:1<61::aid-jcd5>3.0.co;2-w

✦ Synopsis

A blocking set of a design different from a 2-(λ+ 2, λ+ 1, λ) design has at least 3 points. The aim of this note is to establish which 2-(v, k, λ ) designs D with r ≥ 2λ may contain a blocking 3-set. The main results are the following. If D contains a blocking 3-set, then D is one of the following designs: a 2-(2λ + 3, λ+ 1, λ), a 2-(2(λ+ 1), λ+ 1, λ), a 2-(2λ-1, λ , λ), a 2-(4λ+ 3, 2λ+ 1, λ) Hadamard design with λ odd, or a 2-(4λ-1, 2λ , λ) Hadamard design. Moreover a blocking 3-set in a 2-(4λ+ 3, 2λ+ 1, λ ) Hadamard design exists if and only if there is a line with three points. In the case of 2-(4λ-1, 2λ , λ) Hadamard design with λ odd, we give necessary and sufficient conditions for the existence of a blocking 3-set, while in the case λ even, a necessary condition is given.