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A note on 3‐blocked designs
Author(s) -
Berardi Luigia
Publication year - 1997
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1997)5:1<61::aid-jcd5>3.0.co;2-w
Subject(s) - hadamard transform , blocking (statistics) , mathematics , combinatorics , set (abstract data type) , hadamard matrix , block design , line (geometry) , discrete mathematics , arithmetic , computer science , statistics , mathematical analysis , geometry , programming language
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 blocking3‐set, then D is one of the following designs: a 2‐(2λ + 3, λ + 1, λ), a 2‐(2λ + 1),λ + 1, λ), a 2‐(2λ ‐ 1, λ, λ), a 2‐(4λ + 3, 2λ + 1, λ) Hadamard design withλ 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 conditionsfor the existence of a blocking 3‐set, while in the case λ even, a necessary condition is given. ©1997 John Wiley & Sons, Inc.