A flock of a quadratic cone is a partition of a quadratic cone minus its vertex (in 3-dimensional projective space) into plane conics. These objects give rise to a lot of other interesting objects such as translation planes, elation generalized quadrangles, (herds of) ovals, ovoids, regular hyperbolic fibrations, etc. If the associated functions of the field can be written as monomial polynomials, then the flock is called monomial. A semifield flock is one giving rise to a semifield translation plane. The main result of the paper is a geometric computer free construction of the sporadic monomial semifield flock arising from the Penttila-Williams ovoid (using the action of the sporadic Mathieu group \(M_{11}\) on the 11 roots of unity in the Galois field of order \(3^5)\). In contrast, the authors use the computer to proof the uniqueness with respect to being sporadic over a field of characteristic \(p\leq 100\) of order \(p^n\), with \(n\leq 10\). At the end of the paper, some technical general uniqueness and nonexistence results are given, without proof (the proofs are computations which appeared as notes of the Tallini Seminar in Rome (2001)), characterizing for instance the Fisher-Thas-Walker flocks and the Kantor-Payne ones.