The classification of the translation planes of order 16. I (Q788992)

In this paper the translation planes of order 16 are determined. There are precisely eight different isomorphism types. In the proof of this result all sets \(\{T_ 1,...,T_{14}\}\subseteq GL(4,2)\) with the condition that \(T_ iT_ j^{-1}\) (\(i\neq j)\) is fixed-point-free have to be determined. The major tools to bound the computational complexity is (1) the exceptional isomorphism \(A_ 8\simeq GL(4,2)\) and, (2) transformation of such sets into equivalent ones which satisfy certain minimality conditions.