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The authors present three-point and four-point covers having bad reduction at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 12, 18, 28, and 33. By specializing these covers, they obtain number fields ramified at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 11, 12, 17, 18, 25, 28, 30, and 33.

Number Fields with Discriminant ±2a3b and Galois Group An or Sn

Number Fields with Discriminant ±2^a3^b and Galois Group A_n or S_n