Study of BIB (Balanced Incomplete Blocks) Designs through Support Matrices

摘要

This reprint deals with the existence and nonexistence of balanced incomplete block designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given. (Author)