Group divisible designs with block-size four

This paper has been written as Section 6.3 of the paper icj by H. Hanani. All the theorems and lemmas referred to, as well as all the relevant definitions, may be found in [O]. concerning the notation of groups and blocks of a design, we use the convention that if a block is enclosed in &rackets ( ), the points are denoted by exponents of some primitive element, as explained in Section 1 S, while if a block is enclosed in braces ( ), the points themselves are written. We first give a few additions and improvement;s to earlier sections. In the same way as Lemma 2.16 it can be proved: