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_name_46 ( rank INTEGER, attempts VARCHAR, year VARCHAR )

### Question ###
What is the lowest Rank when Attempts was 319, and the Year was larger than 2000?

### Accurate SQL ###

SELECT MIN(rank) FROM table_name_46 WHERE attempts = 319 AND year > 2000