A semifield of order 128 and fractional dimension $\frac{7}{3}$ relative to one of its subsemifields

Ignacio Fernández Rúa, Elías Fernández-Combarro Álvarez

In this short note, an example of a semifield of order 128 containing the Galois field ${\mathbb{F}}_8$ is given. Up to our knowledge, this is the first example supporting the follow…