Some Configurations in Finite Projective Spaces and Partially Balanced Incomplete Block Designs

1965 ◽  
Vol 17 ◽  
pp. 114-123 ◽  
Author(s):  
D. K. Ray-Chaudhuri
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Finite Projective Space ◽  
Block Designs ◽  
Incomplete Block ◽  
Finite Plane ◽  
Balanced Incomplete Block Designs ◽  
Pbib Design ◽  
Finite Projective Spaces ◽  
Balanced Incomplete Block

Using the methods developed in (2 and 3), in this paper we study some properties of the configuration of generators and points of a cone in an w-dimensional finite projective space. The configuration of secants and external points of a quadric in a finite plane of even characteristic is also studied. I t is shown that these configurations lead to several series of partially balanced incomplete block (PBIB) designs. PBIB designs are defined in Bose and Shimamoto (1). A PBIB design with m associate classes is an arrangement of v treatments in b blocks such that.

Non-Existence of Some Unsymmetrical Partially Balanced Incomplete Block Designs

1963 ◽  
Vol 15 ◽  
pp. 686-701 ◽  
Author(s):  
S. S. Shrikhande ◽  
D. Raghavarao ◽  
S. K. Tharthare
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Pbib Design ◽  
Balanced Incomplete Block

A partially balanced incomplete block (PBIB) design with m-associate classes is defined by Bose and Shimamoto (4) as follows:(i) The experimental material is divided into b blocks of k units each, different treatments being applied to the units in the same block.(ii) There are v treatments each of which occurs in r blocks.(iii) There can be established a relation of association between any two treatments satisfying the following requirements.

scholarly journals Construction of balanced incomplete block designs

1977 ◽  
Vol 23 (3) ◽  
pp. 348-353 ◽  
Author(s):  
Elizabeth J. Morgan
Keyword(s):  
Block Design ◽  
Block Designs ◽  
Incomplete Block ◽  
Finite Plane ◽  
Balanced Incomplete Block Design ◽  
Original Design ◽  
Balanced Incomplete Block Designs ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block

AbstractGiven a symmetric balanced incomplete block design or a finite plane, we recursively construct balanced incomplete block designs by taking unions of certain blocks and points of the original design to be the blocks of the new design.

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.

Sign in / Sign up

Export Citation Format

Share Document