A note on the derived semifield planes of order 16.
It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l.
After describing a (general and special) coordinatization of -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in -nets with small degree .