A class of resolvable pairwise balanced designs. (English) Zbl 0611.05008

Rees, Rolf; Wallis, W. D.

Combinatorics, graph theory, and computing, Proc. 17th Southeast. Conf., Boca Raton/Fl. 1986, Congr. Numerantium 55, 211-220 (1986).

[For the entire collection see Zbl 0608.00004.]
A restricted resolvable pairwise balanced design \(R_{\ell}RP(p,k)\) is a pairwise balanced design of index 1 on p treatments with all blocks of size \(\ell\) or \(\ell +1\), such that blocks may be resolved into k parallel classes. We indicate why such designs arise and prove the existence of \(R_ 2RP(p,k)\) whenever \(p\equiv 0\) (mod 6) and p/2\(\leq k\leq p-1\), with the exceptions \((p,k)=(6,3)\) or (12,6). We also give some constructions yielding several infinite families of \(R_ 2RP(p,k)\) for \(p\not\equiv 0\) (mod 6).

MSC:

05B05

Combinatorial aspects of block designs

Keywords:

restricted resolvable pairwise balanced design