On construction of partially balanced n-ary designs

A new method of constructing a series of partially balanced ternary (PBT) designs is presented. In the method, we have added the corresponding rows of incidence matrices of a BIB design and a PBIB design, both obtained from single initial block with at least one element in common between them. The BIB and PBIB designs above were obtained by method of differences. We have also constructed PBT designs and PB n-ary designs from a PBIB design alone based on NCm-scheme as well as from a group divisible PBIB design with smaller number of blocks and moderate block sizes.