Pairwise balanced designs with block sizes 6t + 1

1987 ◽  
Vol 3 (1) ◽  
pp. 365-377 ◽  
Author(s):  
R. C. Mullin ◽  
D. R. Stinson
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

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.

DIRECTED PAIRWISE BALANCED DESIGNS WITH BLOCK SIZES FROM SUBSETS OF {3, 4, …, 10} WHICH CONTAIN 3

2009 ◽  
Vol 01 (04) ◽  
pp. 519-529
Author(s):  
WEIWEI DING ◽  
JIANMIN WANG
Keyword(s):  
Pairwise Balanced Designs ◽  
Single Deletion ◽  
Balanced Designs ◽  
Block Sizes

In this paper we determine completely the spectra of directed pairwise balanced designs with block sizes from any subset of {3, 4, …, 10} which contains 3. Such designs can be used to construct single-deletion/insertion-correcting codes in which the lengths of the codewords may be different.

scholarly journals Pairwise Balanced Designs with Block Sizes 8, 9, and 10

1997 ◽  
Vol 77 (2) ◽  
pp. 228-245 ◽  
Author(s):  
Charles J. Colbourn ◽  
Alan C.H. Ling
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

scholarly journals Super-simple pairwise balanced designs with block sizes 3 and 4

2017 ◽  
Vol 340 (2) ◽  
pp. 236-242
Author(s):  
Guangzhou Chen ◽  
Yong Zhang ◽  
Kejun Chen
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

scholarly journals Class-uniformly resolvable pairwise balanced designs with block sizes two and three

1991 ◽  
Vol 92 (1-3) ◽  
pp. 197-209 ◽  
Author(s):  
Esther Lamken ◽  
Rolf Rees ◽  
Scott Vanstone
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

Pairwise Balanced Designs with Block Sizes Three and Four

1991 ◽  
Vol 43 (4) ◽  
pp. 673-704 ◽  
Author(s):  
Charles J. Colbourn ◽  
Alexander Rosa ◽  
Douglas R. Stinson
Keyword(s):  
Necessary Conditions ◽  
Pairwise Balanced Design ◽  
Balanced Design ◽  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

AbstractGiven integers ν, a and b, when does a pairwise balanced design on ν elements with a triples and b quadruples exist? Necessary conditions are developed, and shown to be sufficient for all v ≥ 96. An extensive set of constructions for pairwise balanced designs is used to obtain the result.

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