  In this paper we construct several new families of quantum codes with good
and asymptotically good parameters. These new quantum codes are derived from
(classical) algebraic geometry (AG) codes by applying the
Calderbank-Shor-Steane (CSS) construction. Many of these codes have large
minimum distances when compared with its code length and they have relatively
small Singleton defect. For example, we construct a family [[46; 2(t_2 - t1);
d]]_25 of quantum codes, where t_1, t_2 are positive integers such that 1 < t_1
< t_2 < 23 and d >= min {46 - 2t_2, 2t_1-2}, of length n = 46, with minimum
distance in the range 2 =< d =< 20, having Singleton defect four. Additionally,
by utilizing t-point AG codes, with t >= 2, we show how to obtain sequences of
asymptotically good quantum codes.
