Balanced ternary designs with block size three, any Λ and any R

Billington E.J. (1985) Balanced ternary designs with block size three, any Λ and any R. Aequationes Mathematicae, 29 1: 244-289. doi:10.1007/BF02189832


Author Billington E.J.
Title Balanced ternary designs with block size three, any Λ and any R
Journal name Aequationes Mathematicae   Check publisher's open access policy
ISSN 0001-9054
Publication date 1985
Sub-type Article (original research)
DOI 10.1007/BF02189832
Volume 29
Issue 1
Start page 244
End page 289
Total pages 46
Publisher Birkhäuser-Verlag
Subject 2600 Mathematics
Abstract A balanced ternary design on V elements is a collection of B blocks (which are multisets) of size K, such that each element occurs 0, 1 or 2 times per block and R times altogether, and such that each unordered pair of distinct elements occurs Λ times. (For example, in the block xxyyz, the pair xy is said to occur four times and the pairs xz, yz twice each.) It is straightforward to show that each element has to occur singly in a constant number of blocks, say ρ1, and so each element also occurs twice in a constant number of blocks, say ρ2, where R=ρ1+2 ρ2. If ρ2=0 the design is a balanced incomplete block design (binary design), so we assume ρ2>0, and K<2 V (corresponding to incompleteness in the binary case). Necessarily Λ>1 if ρ2>0 (and K>2). In 1980 and 1982 the author gave necessary and sufficient conditions for the existence of balanced ternary designs with K=3, Λ=2 and ρ2=1, 2 or 3. In this paper work on the existence of balanced ternary designs with block size three is concluded, in that necessary and sufficient conditions for the existence of a balanced ternary design with K=3, any Λ>1 and any ρ2 are given.
Keyword AMS (1980) subject classification: Primary 05B05, Secondary 62K10
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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