Group divisible designs with three groups and block size four

Group divisible designs with block size four and two groups

We give some constructions of new infinite families of group divisible designs, GDD(n, 2, 4; 1, 2), including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for 3 n 8. For n= 10 there is one missing critical design. If 1> 2, then the necessary conditions are sufficient for n ≡ 4, 5, 8 (mod 12). For each of n=10, 15, 16, 17, 18, 19, and 20 we...

Modified group divisible designs with block size four

The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.

Concerning cyclic group divisible designs with block size three

We determine a necessary and sufficient condition for the existence of a cyclic {3}-GDD with a uniform group size 6n. This provides a fundamental class of ingredients for some recursive constructions which settle existence of k-rotational Steiner triple systems completely.

Odd and even group divisible designs with two groups and block size four

We show the necessary conditions are su6cient for the existence of GDD(n; 2; 4; 1, 2) with two groups and block size four in which every block intersects each group exactly twice (even GDD’s) or in which every block intersects each group in one or three points (odd GDD’s). We give a construction for near 3-resolvable triple systems TS(n; 3; 6) for every n¿ 4, and these are used to provide const...

Resolvable holey group divisible designs with block size three