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Small Uniformly Resolvable Designs for Block Sizes 3 and 4.
- Source :
-
Journal of Combinatorial Designs . Nov2013, Vol. 21 Issue 11, p481-523. 43p. - Publication Year :
- 2013
-
Abstract
- A uniformly resolvable design (URD) is a resolvable design in which each parallel class contains blocks of only one block size k, such a class is denoted k-pc and for a given k the number of k-pcs is denoted rk. In this paper, we consider the case of block sizes 3 and 4 (both existent). We use v to denote the number of points, in this case the necessary conditions imply that v ≡ 0 (mod 12). We prove that all admissible URDs with v < 200 points exist, with the possible exceptions of 13 values of r4 over all permissible v. We obtain a URD({3, 4}; 276) with r4 = 9 by direct construction use it to and complete the construction of all URD({3, 4}; v) with r4 = 9. We prove that all admissible URDs for v ≡ 36 (mod 144), v ≡ 0 (mod 60), v ≡ 36 (mod 108), and v ≡ 24 (mod 48) exist, with a few possible exceptions. Recently, the existence of URDs for all admissible parameter sets with v ≡ 0 (mod 48) was settled, this together with the latter result gives the existence all admissible URDs for v ≡ 0 (mod 24), with a few possible exceptions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10638539
- Volume :
- 21
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Designs
- Publication Type :
- Academic Journal
- Accession number :
- 90054910
- Full Text :
- https://doi.org/10.1002/jcd.21361