Open AccessON THE CONSTRUCTION OF UNIVERSALLY OPTIMAL BLOCK DESIGNS WITH NESTED ROWS AND COLUMNS
Author(s) -
HungLin Fu,
Hsiao-Tien Pao
Publication year - 1996
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.27.1996.4363
Subject(s) - row , row and column spaces , mathematics , block (permutation group theory) , column (typography) , constructive , trace (psycholinguistics) , combinatorics , matrix (chemical analysis) , simple (philosophy) , computer science , geometry , connection (principal bundle) , programming language , linguistics , philosophy , materials science , process (computing) , epistemology , composite material
This paper presents a simple method for constructing universally opti mal block designs with nested rows and columns for number of treatments greater than the number of columns. By allowing a near maximum trace in $\Delta_{v,p,q}$, we pro pose an initial row-column design to achieve a completely symmetric information matrix in much lesser than $v!$ blocks. This constructive method is then extended to the case when balanced incomplete block design is given in the columns.