scholarly journals Optimality of Some Two-Associate-Class Partially Balanced Incomplete-Block Designs

1991 ◽  
Vol 19 (3) ◽  
pp. 1667-1671 ◽  
Author(s):  
C.-S. Cheng ◽  
R. A. Bailey
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Associate Class ◽  
Balanced Incomplete Block

scholarly journals Three-associate class partially balanced incomplete block designs through kronecker product

2020 ◽  
Vol 35 (1-2) ◽  
Author(s):  
Cini Varghese ◽  
Seema Jaggi ◽  
Mohd Harun ◽  
Devendra Kumar
Keyword(s):  
Kronecker Product ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Associate Class ◽  
Balanced Incomplete Block ◽  
Product Of Matrices

Kronecker product of matrices can be advantageously used to obtain three-associate class partially balanced incomplete block (PBIB) designs from two-associate class PBIB designs, for a larger number of treatments. This method has been described here and two such series of PBIB designs are obtained. If the experimenter is constrained of resources, theses designs can be used as an alternative to balanced incomplete block designs or 2-associate class partially balanced incomplete block designs.

Classification of resolvable balanced incomplete block designs — the unitals on 28 points

2009 ◽  
Vol 59 (2) ◽  
Author(s):  
Petteri Kaski ◽  
Patric Östergård
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Doctoral Thesis ◽  
Parallel Class ◽  
Balanced Incomplete Block Designs ◽  
Balanced Incomplete Block

AbstractApproaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points.

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