Group divisible designs with block size five from Clatworthy's table

ABSTRACT

Clatworthy's table (Clatworthy, 1973) lists 37 designs with block size 5 where the number of groups is at the most equal to the block size. Mwesigwa, Sarvate, and Zhang have generalized one of these designs in a recent paper (Mwesigwa et al., 2016). In this note we generalize all but one such design listed in the table. As an aside, we prove that group divisible design with intersection pattern (1, 4) does not exist for any n except for n = 4.

KEYWORDS:

• Group divisible designs
• balanced incomplete block designs
• block intersection patterns.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 05B05
• 05B07
• 62K10

Acknowledgments

The authors thank the referee for helpful suggestions.