Name
Title | ||
|---|---|---|
On the coexistence of conference matrices and near resolvable 2-(2k+1,k,k-1)2-(2k+1,k,k-1) designs |
Abstract | ||
|---|---|---|
We show that a near resolvable 2-(2k+1,k,k-1) design exists if and only if a conference matrix of order 2k+2 does. A known result on conference matrices then allows us to conclude that a near resolvable 2-(2k+1,k,k-1) design with even k can only exist if 2k+1 is the sum of two squares. In particular, neither a near resolvable 2-(21,10,9) design nor does a near resolvable 2-(33,16,15) design exist. For k⩽14, we also enumerate the near resolvable 2-(2k+1,k,k-1) designs and the corresponding conference matrices. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.jcta.2005.05.005 | Journal of Combinatorial Theory, Series A |
Keywords | DocType | Volume |
Conference matrix,near resolvable balanced incomplete block design,NRB,NRBIBD | Journal | 113 |
Issue | ISSN | Citations |
4 | 0097-3165 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |