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

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 \( 3 \leq k \leq 13 \). 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 \( 3 \leq k \leq 8 \) and there are respectively 2, 0, 19, 8, and 374 nonisomorphic designs for \( k = 9, 10, 11, 12 \), and \( 13 \).