## Abstract

Balanced incomplete block designs, or BIBDs, have been studied for many years. In a famous 115 page paper Haim Hanani completely settled the existence question for BIBDs with block size less than 6. In the same paper he settled this question for block size 6 and λ > 1. However when the block size is 6 and λ = 1 the whole question becomes much more difficult. In the present paper we discuss the work that has been done on this. There are, at present, 55 values of υ for which the existence of such a design is in doubt. We will show how the remaining values of υ are handled.

## Keywords

Automorphism Group Base Block Large Block Prime Power Cube Root
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© Springer Science+Business Media Dordrecht 1996