an:02173305
Zbl 1062.05035
Yin, Jianxing
Kirkman packing and covering designs with spanned holes of size 2
EN
J. Comb. Des. 13, No. 3, 173-183 (2005).
00115717
2005
j
05B40
Summary: A Kirkman holey packing (resp. covering) design, denoted by KHPD\((g^u)\) (resp. KHCD\((g^u)\)), is a resolvable (\(gu\), 3, 1) packing (resp. covering) design of pairs with \(u\) disjoint holes of size \(g\), which has the maximum (resp. minimum) possible number of parallel classes. Each parallel class contains one block of size \(\delta\), while other blocks have size 3. Here \(\delta\) is equal to 2, 3, and 4 when \(gu \equiv 2, 3\), and 4 (mod 3) in turn. In this paper, the existence problem of a KHPD\((2^u)\) and a KHCD\((2^u)\) is solved with one possible exception of a KHPD(\(2^8\)).