Abstract
For a given number of varieties v, number of blocks b, common treatment replication r and common block size k, rv = bk, 3 ≤ k ≤ 8, k ≤ v, necessary conditions for the existence of p-trend-free equireplicated binary block designs are derived for 2 ≤ p ≤ k - 1. The conditions are also sufficient for complete block designs (where v = k and b = r). For balanced incomplete block designs (BIBDs) that satisfy the necessary conditions, we investigate whether varieties can be ordered within blocks to make the designs p-trend-free. For v ≤ 20 and b ≤ 100, if the necessary conditions are satisfied and if a BIBD exists, we conclude that a p-trend-free BIBD is also available.
Original language | English (US) |
---|---|
Pages (from-to) | 65-78 |
Number of pages | 14 |
Journal | Utilitas Mathematica |
Volume | 56 |
State | Published - Nov 1999 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics