For positive integers n,q,t we determine the maximum number of integer sequ
ences (a(1),...,a(n)) which satisfy 1 less than or equal to a(i) less than
or equal to q for 1 less than or equal to i less than or equal to n, and an
y two sequences agree in at least t positions. The result gives an affirmat
ive answer to a conjecture of Frankl and Furedi.