Enumeration of all (2k + 1;k;k 1)-NRBIBDs for 3 k 13

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 k 13. We rst 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 k 8 and there are respectively 2, 0, 19, 8 and 374 nonisomorphic designs for k = 9, 10, 11, 12 and 13.