Extensions of Generalized Product Caps

We give some variants of a new construction for caps. As an application of these constructions, we obtain a 1216-cap in PG (9,3) a 6464-cap in PG (11,3) and several caps in ternary affine spaces of larger dimension, which lead to better asymptotics than the caps constructed by Calderbank and Fishburn [1]. These asymptotic improvements become visible in dimensions as low as 62, whereas the bound from Calderbank and Fishburn [1] is based on caps in dimension 13,500.