共查询到20条相似文献,搜索用时 31 毫秒
1.
Geometriae Dedicata - A simple sufficient condition for embedding of a quasiresidual balanced incomplete block design into the corresponding symmetric balanced incomplete block design is obtained. 相似文献
2.
When basic necessary conditions for the existence of a balanced incomplete block design are satisfied, the design may still not exist or it may not be known whether it exists. In either case, other designs may be considered for the same parameters. In this article we introduce a class of alternative designs, which we will call virtually balanced incomplete block designs. From a statistical point of view these designs provide efficient alternatives to balanced incomplete block designs, and from a combinatorial point of view they offer challenging new questions. © 1995 John Wiley & Sons, Inc. 相似文献
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It is shown that a partial geometric design with parameters (r, k, t, c) satisfying certain conditions is equivalent to a two-class partially balanced incomplete block design. This generalizes a result concerning partial geometric designs and balanced incomplete block designs. 相似文献
5.
Sanpei Kageyama 《Journal of Combinatorial Theory, Series A》1974,17(2):269-272
Blackwelder (1969) has given two methods of constructing balanced incomplete block (BIB) designs from the association matrices of association schemes with two and three associate classes. In this note these two methods are incorporated in a general method, and the existence of a series of BIB designs is shown by the generalized method. In addition, a remark about partially balanced incomplete block (PBIB) designs with respect to the method is made. 相似文献
6.
In [[6] Riv. Mat. Univ. Parma 11 (2) (1970) 79-96] Ferrero demonstrates a connection between a restricted class of planar nearrings and balanced incomplete block designs. In this paper, bearing in mind the links between planar nearrings and weakly divisible nearrings (wd-nearrings), first we show the construction of a family of partially balanced incomplete block designs from a special class of wd-nearrings; consequently, we are able to give some formulas for calculating the design parameters. 相似文献
7.
Sanpei Kageyama 《Annals of the Institute of Statistical Mathematics》1980,32(1):255-261
Summary It is well known that the connected incomplete block designs with the highest intrablock efficiency factors are balanced.
In a connected balanced block (BB) design, every elementary contrast is estimated with the same variance. If a treatment is
lost in a connected BB design, then the residual design is not balanced for the most part. In this paper, an upper bound and
a lower bound for efficiency of a residual design are derived with some illustrations. Moreover, from these discussions it
is conceivable that the loss of efficiency even in the unbalanced case is, in general, small. 相似文献
8.
《Discrete Mathematics》2002,231(1-3):91-119
Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric balanced nested balanced incomplete block designs with block size 3 and 4. 相似文献
9.
The necessary and sufficient conditions for the existence of simple incomplete block design (v, w; 4,2)-IPBDs are determined. As a consequence, the necessary and sufficient conditions for the embeddings of simple two-fold balanced incomplete block designs with block size 4 are also determined. 相似文献
10.
A. Dey 《Annals of the Institute of Statistical Mathematics》1970,22(1):389-393
Summary A method of construction of balanced ternary designs using affine α-resolvable balanced incomplete block designs is presented. 相似文献
11.
Construction of nested balanced incomplete block (BIB) designs, nested balanced ternary designs and rectangular designs from given nested BIB designs and resolvable BIB designs are described. New constructions ofq-ary codes from nested BIB designs and balanced bipartite weighing designs are also given. 相似文献
12.
Donovan Diane Price Aiden Rao Asha Üsküplü Elif ŞYazıcı Emine 《Journal of Algebraic Combinatorics》2022,55(1):259-275
Journal of Algebraic Combinatorics - This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from partially balanced incomplete block designs. Since... 相似文献
13.
Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.AMS Classification:05B05, 05B30 相似文献
14.
Beiliang Du 《组合设计杂志》2004,12(6):404-420
Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., (v, 3k, λ)‐splitting BIBDs; we give the spectrum of (v, 3 × 2, λ)‐splitting BIBDs. As an application, we obtain an infinite class of 2‐splitting A‐codes. © 2004 Wiley Periodicals, Inc. 相似文献
15.
Summary The purpose of this paper is three-fold. The first purpose is to compile and to systematize published and dispersed results
on two aspects of balancing in incomplete block designs, i.e., pairwise balance and variance balance. This was done in order
to establish the status of these two concepts of balance in published literature and to put them in a form which is useful
for further work in this area. Also, the results in this form are necessary for the development of the remainder of the paper.
The second purpose of this paper is to present a method of constructing unequal replicate and/or unequal block size experiment
designs for which the variance balance property is achieved. The method of construction involves the union of blocks from
two or more block designs and the augmentation of some of the blocks with additional treatments; the method is denoted asunionizing block designs. A straight-forward extension of the method would produce a partially balanced block design with unequal replicate and/or
unequal block designs. The enlargement of the concept and availability of variance blanced block designs to accommodate unequal
replication and/or unequal block sizes is important to the researcher, the teacher, and the experimenter needing such designs.
For example, an animal nutritionist or a psychologist is no longer required to have constant litter or family sizes for the
blocks and may have unequal replication on the treatments for those treatments with insufficient material and still attain
the goal of equal variances on all normalized treatment contracts.
The third purpose of the paper is to apply the unionizing block designs method to construct a family of unequal replicate
and unequal block size variance balanced designs. Some comments are given on the extension of the unionizing block designs
method to construct other families of variance balanced or partially balanced block designs.
This investigation was supported in part by PHS Research Grant No. R01-GM-05900 from General Medical Services. 相似文献
16.
Subir Ghosh Sanpei Kageyama Rahul Mukerjee 《Annals of the Institute of Statistical Mathematics》1992,44(3):593-603
In this paper the problem of finding the design efficiency is considered when a single observation is unavailable in a connected binary block design. The explicit expression of efficiency is found for the resulting design when the original design is a balanced incomplete block design or a group divisible, singular or semiregular or regular with 1>0, design. The efficiency does not depend on the position of the unavailable observation. For a regular group divisible design with 1>0, the efficiency depends on the position of the unavailable observation. The bounds, both lower and upper, on the efficiency are given in this situation. The efficiencies of designs resulting from a balanced incomplete block design and a group divisible design are in fact high when a single observation is unavailable.The work of the first author is sponsored by the Air Force Office of Scientific Research under Grant AFOSR-90-0092.On leave from Indian Statistical Institute, Calcutta, India. The work of the third author was supported by a grant from the CMDS, Indian Institute of Management, Calcutta. 相似文献
17.
Robert Bruce Brown 《Journal of Combinatorial Theory, Series A》1975,19(1):115-116
A balanced incomplete block design with parameters (16, 24, 9, 6, 3) is described in which every pair of blocks intersects in at most three varieties. However, the design cannot be extended to a symmetric design with parameters (25, 25, 9, 9, 3). 相似文献
18.
In this paper we define a 2-adjugate mod 2 class of designs obtained by application of process of 2-adjugation to the incidence matrix of given design and subsequently reducing to modulo 2. General properties of such designs are discussed and its application to the class of unreduced Balanced Incomplete Block Designs is investigated in detail. It is found that in this case we obtain a class of generalized partially balanced incomplete block designs with 2 associate classes and with triangular association scheme, but with unequal block sizes. 相似文献
19.
Richard M Wilson 《Journal of Combinatorial Theory, Series A》1983,34(3):313-324
A number of inequalities concerning the set structure of balanced incomplete block designs are unified, and strengthened in the case of t designs with t ? 4. 相似文献
20.
Motivated by the field experimental designs in agriculture, the theory of block designs has been applied to several areas such as statistics, combinatorics, communication networks, distributed systems, cryptography, etc. An explicit formula and its fast computational algorithm for a class of symmetric balanced incomplete block designs are presented. Based on the formula and the careful investigation of the modulus multiplication table, the algorithm is developed. The computational costs of the algorithm is superior to those of the conventional ones. 相似文献