what is the minimial of cells required to form a p-local type n complex? i've been told that it's 2^n (i assume at p=2), but i don't know why this is true

nvm i see why this is true, the generalized moore spectra should give a sharp bound

but they definitely don't give the best total dimension, right?

This question has come up here before, and I don't recall the argument that the cofiber of a (self-)map of spectra of type n cannot somehow jump to be of type n + k for k > 1. generalized Moore spectra realize the growth formula you've been told, but they don't demonstrate minimality on their own

@skd I don't think that makes it a complete proof: the lemma only talks about self-maps

And moreover it is false when the dimension of the self-map is 0

(i'm still glad to know about that argument tho)

@TylerLawson I just found this and it saved me a chunk of time. Thanks for putting those thoughts publicly!