| Abstract: | Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable  ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable  ‐BIBDs are  (mod  ) and  . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable  ‐RBIBD, namely  (mod  ) and  , are sufficient. A few new pairwise balanced designs are also given. |
