On Theory and Applications of BIB Designs with Repeated Blocks.

摘要: Consider BIB designs with parameters $v, b, r, k$ and $\lambda$. Define the support of a design to be set its distinct blocks let cardinality $b^\ast$. If $b^\ast < b$ then is said repeated blocks. Some potential applications such experimental controlled sampling are given. necessary sufficient conditions for existence these some algorithms their constructions provided. Bounds on $b^\ast$ have been obtained. A condition under which can found. table $22 \leqq b^\ast 56$ $v = 8$ $k 3$ included.