Any State dissatisfied with a final determination of the Secretary pursuant to § 201.4 or § 201.6(a) may, within 60 days after it has been notified of such determination, file with the U.S. Court of Appeals for the circuit in which such State is located a petition for review of such determination. After a copy of the petition is transmitted by the clerk of the court to the Secretary, the Secretary thereupon shall file in the court the record of proceedings upon which such determination was based as provided in section 2112 of title 28, United States Code. The court is bound by the Secretary's findings of fact, if supported by substantial evidence. The court has jurisdiction to affirm the Secretary's decision, or set it aside in whole or in part, or, for good cause, to remand the case for additional evidence. If the case is remanded, the Secretary may thereupon make new or modified findings of fact, and may modify his previous determination. The Secretary shall certify to the court the transcript and record of the further proceedings. The judgment of the court is subject to review by the Supreme Court of the United States upon certiorari or certification as provided in 28 U.S.C. 1254.