Enumeration of 2-(9,3,\lambda) designs and their resolutions (2002)
AUTHORS:
Östergård Patric R. J.,
Kaski Petteri
JOURNAL:
Designs, Codes and Cryptography
VOLUME:
27
PAGES:
131--137
URL:
http://dx.doi.org/10.1023/A:1016558720904
@article{ OsKa02, author = {{\"O}sterg{\aa}rd, Patric R. J. and Kaski, Petteri}, title = "Enumeration of 2-(9,3,\lambda) designs and their resolutions", url = "http://dx.doi.org/10.1023/A:1016558720904", journal = "Designs, Codes and Cryptography", abstract = "We consider $2$-$(9,3,\lambda)$ designs, which are known to exist for all $\lambda\geq 1$, and enumerate such designs for $\lambda=5$ and their resolutions for $3\leq\lambda\leq 5$, the smallest open cases. The number of nonisomorphic such structures obtained is $5\,862\,121\,434$, $426$, $149\,041$, and $203\,047\,732$, respectively. The designs are obtained by an orderly algorithm, and the resolutions by two approaches: either by starting from the enumerated designs and applying a clique-finding algorithm on two levels or by an orderly algorithm.", volume = "27", year = "2002", keywords = "automorphism group, {B}{I}{B}{D}, orderly algorithm, resolved design", pages = "131--137" }