Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Steiner triple systems of order 21 with a transversal subdesign
  TD(3,6)   We prove several structural properties of Steiner triple systems (STS) of
order 3w+3 that include one or more transversal subdesigns TD(3,w). Using an
exhaustive search, we find that there are 2004720 isomorphism classes of
STS(21) including a subdesign TD(3,6), or, equivalently, a 6-by-6 latin square.

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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph