Enumeration of all $(2k+1,k,k-1)$-NRBIBDs for $3\le k\le 13$

Abstract

A backtracking over near parallel classes with an early isomorph rejection is carried out to enumerate all the near resolvable $(2k+1,k,k-1)$ balanced incomplete block designs for $3\le k\le 13$. We first prove some results which enable us to restrict the search space of near parallel classes. The number of nonisomorphic designs is equal to 1 for each $3\le k\le 8$ and there are respectively 2, 0, 19, 8, and 374 nonisomorphic designs for $k=9,10,11,12$, and $13$.