The number oft-wise balanced designs

COMBINATORICA ◽  
1991 ◽  
Vol 11 (3) ◽  
pp. 207-218 ◽  
Author(s):  
Charles J. Colbourn ◽  
Dean G. Hoffman ◽  
Kevin T. Phelps ◽  
Vojt?ch R�dl ◽  
Peter M. Winkler
Keyword(s):  
Balanced Designs

A Class of E-Optimal Proper Efficiency-Balanced Designs

Biometrika ◽  
1991 ◽  
Vol 78 (3) ◽  
pp. 693
Author(s):  
Ashish Das ◽  
Sanpei Kageyama
Keyword(s):  
Proper Efficiency ◽  
Balanced Designs

scholarly journals Pairwise balanced designs and sigma clique partitions

2016 ◽  
Vol 339 (5) ◽  
pp. 1450-1458 ◽  
Author(s):  
Akbar Davoodi ◽  
Ramin Javadi ◽  
Behnaz Omoomi
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs

scholarly journals Pairwise balanced designs from finite fields

1999 ◽  
Vol 208-209 ◽  
pp. 103-117 ◽  
Author(s):  
Marco Buratti
Keyword(s):  
Finite Fields ◽  
Pairwise Balanced Designs ◽  
Balanced Designs

Balanced designs for two-component competition experiments on a square lattice

Euphytica ◽  
1980 ◽  
Vol 29 (2) ◽  
pp. 459-464 ◽  
Author(s):  
A. Veevers ◽  
M. Zafar-Yab
Keyword(s):  
Square Lattice ◽  
Two Component ◽  
Balanced Designs

Optimal variance- and efficiency-balanced designs for one- and two-way elimination of heterogeneity

Metrika ◽  
1991 ◽  
Vol 38 (1) ◽  
pp. 227-238 ◽  
Author(s):  
A. Das ◽  
A. Dey
Keyword(s):  
Balanced Designs

scholarly journals Some Pairwise Balanced Designs

10.37236/1491 ◽  
1999 ◽  
Vol 7 (1) ◽  
Author(s):  
Malcolm Greig
Keyword(s):  
Block Design ◽  
Basis Sets ◽  
Combinatorial Designs ◽  
Pairwise Balanced Design ◽  
Balanced Design ◽  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

A pairwise balanced design, $B(K;v)$, is a block design on $v$ points, with block sizes taken from $K$, and with every pair of points occurring in a unique block; for a fixed $K$, $B(K)$ is the set of all $v$ for which a $B(K;v)$ exists. A set, $S$, is a PBD-basis for the set, $T$, if $T=B(S)$. Let $N_{a(m)}=\{n:n\equiv a\bmod m\}$, and $N_{\geq m}=\{n:n\geq m\}$; with $Q$ the corresponding restriction of $N$ to prime powers. This paper addresses the existence of three PBD-basis sets. 1. It is shown that $Q_{1(8)}$ is a basis for $N_{1(8)}\setminus E$, where $E$ is a set of 5 definite and 117 possible exceptions. 2. We construct a 78 element basis for $N_{1(8)}$ with, at most, 64 inessential elements. 3. Bennett and Zhu have shown that $Q_{\geq8}$ is a basis for $N_{\geq8}\setminus E'$, where $E'$ is a set of 43 definite and 606 possible exceptions. Their result is improved to 48 definite and 470 possible exceptions. (Constructions for 35 of these possible exceptions are known.) Finally, we provide brief details of some improvements and corrections to the generating/exception sets published in The CRC Handbook of Combinatorial Designs.

scholarly journals On MSE-Optimal Circular Crossover Designs

2021 ◽  
Vol 15 (4) ◽  
Author(s):  
C. Neumann ◽  
J. Kunert
Keyword(s):  
Optimal Design ◽  
Mean Square Error ◽  
Current Treatment ◽  
Mean Square ◽  
Crossover Designs ◽  
Carryover Effects ◽  
Circular Structure ◽  
Balanced Designs ◽  
Preceding Period ◽  
The Mean

AbstractIn crossover designs, each subject receives a series of treatments, one after the other in p consecutive periods. There is concern that the measurement of a subject at a given period might be influenced not only by the direct effect of the current treatment but also by a carryover effect of the treatment applied in the preceding period. Sometimes, the periods of a crossover design are arranged in a circular structure. Before the first period of the experiment itself, there is a run-in period, in which each subject receives the treatment it will receive again in the last period. No measurements are taken during the run-in period. We consider the estimate for direct effects of treatments which is not corrected for carryover effects. If there are carryover effects, this uncorrected estimate will be biased. In that situation, the quality of the estimate can be measured by the mean square error, the sum of the squared bias and the variance. We determine MSE-optimal designs, that is, designs for which the mean square error is as small as possible. Since the optimal design will in general depend on the size of the carryover effects, we also determine the efficiency of some designs compared to the locally optimal design. It turns out that circular neighbour-balanced designs are highly efficient.

Constructions of Pairwise-and Variance-Balanced Designs

Statistics ◽  
1997 ◽  
Vol 29 (3) ◽  
pp. 241-250
Author(s):  
Kishore Sinha ◽  
Byron Jones ◽  
Sanpei Kageyama
Keyword(s):  
Balanced Designs

Mixture discrepancy on symmetric balanced designs

2015 ◽  
Vol 104 ◽  
pp. 123-132 ◽  
Author(s):  
A.M. Elsawah ◽  
Hong Qin
Keyword(s):  
Balanced Designs

Partially Balanced Designs

2014 ◽  
Author(s):  
Rosemary A. Bailey
Keyword(s):  
Balanced Designs
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