The director of property valuation shall examine the tax assessment and appraisal of taxable property of the various counties prior to September 15 each year. On or before such date, the director shall publish a list of those counties which the director finds to be in substantial compliance with the requirements of law to appraise taxable property of all counties at fair market value in money as defined by Kan. Stat. Ann. § 79-503a, and amendments thereto. Such list shall also specify those counties which are not in substantial compliance with the law and every county shall be named in one or the other parts of such list. After such list has been initially published, the board of county commissioners of any county may petition the director of property valuation to reconsider the determination as published in such list. Such petition shall be made in compliance with rules and regulations adopted by the secretary of revenue as to the form and contents of any such petition. Such rules and regulations shall provide for a redetermination, in every case, after the final completion of any countywide reappraisement. The director of property valuation may make a redetermination as to any county whether the same is petitioned for or not.