Large caps in projective space PG(r,4)

A computer-supported recursive construction for large caps in projective space PG(r,4) is presented. Using this recursive construction, we construct a 2136-cap in PG(8,4), a 5124-cap in PG(9,4), a 15840-cap in PG(10,4), a 36084-cap in PG(11,4) and a 95256-cap in PG(12,4). The first four caps are larger than the known largest 2110-cap, 5040-cap, 15423-cap and 34566-cap respectively. Then we propose a fast algorithm for checking completeness of a cap based on a bijective map φ between points in PG(r,4) and a subset I of the positive integer set N. Completeness of the new caps is checked.