Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect Graeco-Latin balanced incomplete block designs and related
  designs   Main effect plans orthogonal through the block factor (POTB) have been
defined and a few series of them have been constructed in Bagchi (2010). These
plans are very closely related to the `mutually orthogonal balanced nested
row-column designs' of Morgan and Uddin (1996) and many other combinatorial
designs in the literature with different names like `BIBDs for two sets of
treatment', `Graeco-Latin designs' and `PERGOLAs'. In fact all of them may be
viewed as POTBs satisfying one or more additional conditions, making them
`optimal'. However, the PERGOLAs are defined to satisfy an additional property,
without which also it is optimal. Interestingly, this additional property is
satisfied by all the hitherto known examples of POTBs, even when their
definitions do not demand it. In this paper we present direct and recursive
constructions of POTBs. In the process we have constructed one design which
seems to be the first example of an `optimal' two-factor POTB which is not a
PERGOLA (see Theorem \ref {POTB2}).

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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: stat