ABSTRACT
Theorem 93.1. Let pi be a translation plane with spread S in PG(3, q). Let F denote the associated field of order q and let K be a quadratic extension field with basis {1, θ} such that θ2 = θα + β for α, β ∈ F . Choose any quasifield and write the spread as follows:
x = 0, y = x
[ g(t, u) h(t, u)− αg(t, u) = f(t, u) t u
] ∀t, u ∈ F
where g, f and unique functions on F × F and h is defined as noted in the matrix, using the term α.
