| 31. | The best known upper bound, not improved since the 1970s, is.
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| 32. | First an upper bound on the number of solutions is computed.
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| 33. | N rather than if there is an upper bound on N.
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| 34. | Martin said at a news conference, calling it an " upper bounds " estimate.
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| 35. | The existential version of the Local Lemma permits a larger upper bound on dependencies:
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| 36. | A bound of type UP means an upper bound is applied to the variable.
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| 37. | The proof of the theorem provides only an upper bound.
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| 38. | The upper bound was later improved by Laurent Bartholdi to
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| 39. | Still, the size of the hypergraph yields first upper bounds.
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| 40. | This gives an upper bound of about 250 Ma.
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