### Recursive Methods for Construction of Balanced N-ary Block Designs

2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10. This paper presents a recursive method for the construction of balanced n-ary block designs. This method is based on the analogy between a balanced incomplete binary block design (B.I .E .B) and the set of all distinct linear sub-varieties of the same dimension extracted from a finite projective geometry. If V1 is the first B.I .E .B resulting from this projective geometry, then by regarding any block of V1 as a...