New Quantum Codes Constructed by Quantum Caps in PG(3,9) and PG(4,9)

In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps in
$PG(3,9)$
and
$PG(4,9)$
are constructively proven to exist. Then, according to the theorem that each quantum cap corresponds to a quantum error-correcting code with
$d=4$
, we obtain 278 quantum error-correcting codes. Most of these results break the GV bound, and a number of them are optimal quantum codes or have improved parameters.