Non-archimedean Banach spaces of universal disposition

A space of universal disposition is a Banach space which has certain natural extension properties for isometric embeddings of Banach spaces belonging to a specific class. We study spaces of universal disposition for non-archimedean Banach spaces. In particular, we introduce the classification of non-archimedean Banach spaces depending on the cardinality of maximal orthogonal sets, which can be viewed as a kind of special density and characterize spaces of universal disposition for each distinguished class.