Group divisible designs with block size five from Clatworthy’s table. (English) Zbl 1392.05016
In W. H. Clatworthy’s table [Tables of two-associate-class partially balanced designs. Washington: U.S.Department of Commerce, National Bureau of Standards (1973; Zbl 0289.05017)] there is a list of 37 designs with block size 5 where the number of groups is at most equal to the block size. R. Mwesigwa, D. G. Sarvate and L. Zhang [“Group divisible designs of four groups and block size five with configuration (1,1,1,2)”, J. Algebra Comb. Discrete Struct. Appl. 3, No. 3, 187–194 (2016)] have generalized one of these designs.
In this paper, the authors generalize all but one such design and give a complete list of tables with specified remarks. Moreover, they prove that a group divisible design \((n,4,5; \frac{9n}{n-1},2)\) with intersection pattern (1,4) does not exist for any \(n\), except for \(n=4\).
In this paper, the authors generalize all but one such design and give a complete list of tables with specified remarks. Moreover, they prove that a group divisible design \((n,4,5; \frac{9n}{n-1},2)\) with intersection pattern (1,4) does not exist for any \(n\), except for \(n=4\).
Reviewer: Andrea Svob (Rijeka)
MSC:
| 05B05 | Combinatorial aspects of block designs |
| 05B07 | Triple systems |
| 62K10 | Statistical block designs |
Citations:
Zbl 0289.05017References:
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