Balanced Incomplete Block Designs with Block Size 7.

The object of this paper is the construction of balanced incomplete block designs with k=7. This paper continues the work begun by Hanani, who solved the construction problem for designs with a block size of 7, and with λ=6, 7, 21 and 42. The construction problem is solved here for designs with λ > 2 except for v=253, λ= 4,5 ; also for λ= 2, the number of unconstructed designs is reduced to 9 (1 nonexistent, 8 unknown). [ABSTRACT FROM AUTHOR]