Bounds for the number of common symbols in balanced and certain partially balanced designs
نویسندگان
چکیده
منابع مشابه
Balanced nested designs and balanced arrays
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 bal...
متن کاملBalanced Nested Designs and Balanced n-ary Designs
We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (1972). By use of these constructions, we show some constructions for regu...
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We propose two deterministic key predistribution schemes in a Wireless Sensor Network (WSN), in which sensor nodes are deployed randomly. Both the schemes are based on Partially Balanced Incomplete Block Designs (PBIBD). An important feature of our scheme is that every pair of nodes can communicate directly, making communication faster and efficient. The number of keys per node is of the order ...
متن کاملOn construction of partially balanced n-ary designs
A new method of constructing a series of partially balanced ternary (PBT) designs is presented. In the method, we have added the corresponding rows of incidence matrices of a BIB design and a PBIB design, both obtained from single initial block with at least one element in common between them. The BIB and PBIB designs above were obtained by method of differences. We have also constructed PBT de...
متن کاملBalanced ternary designs with holes and numbers of common triples
There exists a balanced ternary design with block size 3 and index 2 on 2v P2 + 4 and 2v P2 + 1 elements with a hole of size v, for all positive integers v and P2, such that v ~ 2P2 + 1. As an application of this result, we determine the numbers of common triples in two simple balanced ternary designs with block size 3 and index 2, for P2 = 3 and 4.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1977
ISSN: 0097-3165
DOI: 10.1016/0097-3165(77)90078-4