Existence of OBIBDs with \(k=4\) with and without nesting (Q1810624)
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scientific article; zbMATH DE number 1924752
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of OBIBDs with \(k=4\) with and without nesting |
scientific article; zbMATH DE number 1924752 |
Statements
Existence of OBIBDs with \(k=4\) with and without nesting (English)
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9 June 2003
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New closure results for the existence of pairwise balanced designs are established for a number of sets of block sizes. In particular, a strong result is obtained for the set of block sizes \(\{8,9\}\), and this is used to obtain a closure for the set of all prime powers congruent to \(0\) or \(1\) modulo \(4\) and at least \(8\). These closure results are then employed to settle (with finitely many exceptions) existence questions for nested designs of block size four with subblocks of size two, and for certain balanced incomplete block designs with ``adjusted orthogonality'' (OBIBDs).
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nested BIBD
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OBIBD
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ONBIBD
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PBD
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