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D‐optimal designs and group divisible designs
Author(s) -
Tamura Hiroki
Publication year - 2006
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/jcd.20103
Subject(s) - mathematics , combinatorics , group (periodic table) , matrix (chemical analysis) , block (permutation group theory) , order (exchange) , block design , discrete mathematics , arithmetic , chemistry , materials science , organic chemistry , finance , economics , composite material
We obtain new conditions on the existence of a square matrix whose Gram matrix has a block structure with certain properties, including D‐optimal designs of order $n\equiv 3 \pmod 4$ , and investigate relations to group divisible designs. We also find a matrix with large determinant for n = 39. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 451–462, 2006