A computer algorithm for generating 3-designs by the method of trade off. (English) Zbl 0937.62632
Summary: The set of all distinct blocks in a \(t\)-design is referred to as the support of the design, and its cardinality is denoted by \(b^*\). To determine the range of \(b^*\), for all \(t\)-designs with the parameters \(v\) and \(k\), is an open question. One of the methods in the literature for answering this question is the method of trade off. In this note we introduce a computer algorithm for trade off methodology on 3-designs. The method of 2-trade off is included in this algorithm as a special case.
MSC:
| 62K10 | Statistical block designs |
| 05-04 | Software, source code, etc. for problems pertaining to combinatorics |
References:
| [1] | Graham, R.L.; Li, S.Y.R.; Li, W.C.W.: On the structure of t-designs. SIAM J. Algebraic and discrete methods 1, 8-14 (1980) · Zbl 0499.05012 |
| [2] | Hedayat, A.; Li, S.Y.R.: The trade-off method in construction of BIB designs with variable support sizes. Ann. statistics 7, 1277-1287 (1979) · Zbl 0424.62052 |
| [3] | Hwang, H.L.: On the structure of (v, k, t) trades. J. statist. Plann. inference 13, 179-191 (1986) · Zbl 0593.62071 |
| [4] | Khosrovshahi, G.B.; Mahmoodian, E.S.: A computer algorithm for trade-off methodology and tradability in block designs. Technical report no. 1-1366 (1987) |
| [5] | Mahmoodian, E.S.: On the support size of 3-designs with repeated blocks. Ars combinatoria 30, 13-22 (1990) · Zbl 0768.05009 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
