Non-isomorphic Affine Finites $\langle Bb,E \rangle$-nets

Alija Mandak

Mathematica Moravica, Tome 1 (1997) no. 1.

Résumé

It is known that for each $n\in \mathbb{N}$ there exist affine finites $\langle Nn,E\rangle$-nets $(A_{n-1}(n,q),\parallel )$ with parameters $(q,q^{n-1}+q^{n-2}+\cdots+q+1,q^{n-2})$, where $q$ is prime power. In the paper we prove that for each $n\in\mathbb{N}$, $n>2$ and any prime power $q$ there exist non-isomorphic affine finites $\langle Nn,E\rangle$-nets with equal parameters $(q,q^{n-1}+q^{n-2}+\cdots+q+1,q^{n-2})$.