On constructions for two dimensional balanced sampling plan excluding contiguous units with block size four. (English) Zbl 1147.05017
A (two-dimensional) balanced sampling plan excluding contiguous units 2-BSEC\((n,m,k,\lambda)\) has point set \({\mathbb Z}_n \times {\mathbb Z}_m\), where two points \((a_1,b_1)\) and \((a_2,b_2)\) are 2-contiguous when \(a_1=a_2\) and \(b_1 \equiv b_2 \pm 1 \pmod{m}\), or \(a_1 \equiv a_2 \pm 1 \pmod{n}\) and \(b_1=b_2\). The BSEC has a collection \(\mathcal B\) of \(k\)-subsets of points so that no 2-contiguous points appear together in a block, and every pair of points that are not 2-contiguous occur together in exactly \(\lambda\) blocks. In this paper, cases with \(k=4\) are treated and substantial partial results are obtained.
Reviewer: Charles J. Colbourn (Tempe)
MSC:
| 05B05 | Combinatorial aspects of block designs |
Keywords:
balanced sampling plan exluding contiguous units; BSEC; group divisible design; modified group divisible designReferences:
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