  This article derives lower bounds on the supremal (strict) p-negative type of
finite metric spaces using purely elementary techniques. The bounds depend only
on the cardinality and the (scaled) diameter of the underlying finite metric
space. Examples show that these lower bounds can easily be best possible under
clearly delineated circumstances. We further point out that the entire theory
holds (more generally) for finite semi-metric spaces without modification and
wherein the lower bounds are always optimal.
