Section 38A. The board of registrars of voters of every city or town shall submit to the state secretary a count for each precinct of the number of voters enrolled in each political party and each political designation and the number of unenrolled voters. The count shall be correct as of the last day to register voters under section twenty-six of chapter fifty-one before every regular state and presidential primary and biennial state election, and in an even-numbered year in which no presidential primary is held, also as of February first. The secretary shall receive the count in writing not later than ten days after each such date, and shall issue a report thereof.