Trend-free block designs for higher order trends

Feng Shun Chai, John Stufken

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish (US)
Pages (from-to)65-78
Number of pages14
JournalUtilitas Mathematica
StatePublished - Nov 1999
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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