Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE table_66181 ( "Year" real, "LPGA wins" real, "Earnings ($)" real, "Money list rank" real, "Average" real )

### Question ###
When earnings ($) is more than 583,796 after 1998 with 1 LPGA wins and greater than 10 Money list rank, what is the smallest average?

### Accurate SQL ###

SELECT MIN("Average") FROM table_66181 WHERE "Year" > '1998' AND "Earnings ($)" > '583,796' AND "LPGA wins" = '1' AND "Money list rank" > '10'