Some Friends of Alltop’s Designs $4-(2^f+1,5,5)$

Abstract

We construct several families of simple 4-designs, which are closely related to Alltop’s series with parameters $4-(2^f+1,5,5)$, $f$ odd. More precisely, for every $q=2^f$, where $gcd(f,6)=1$, $f\ge 5$, we construct designs with the following parameters:

$$4-(q+1,6,\lambda ),\text{where}\lambda \in \{60,70,90,100,150,160\},$$
$$4-(q+1,8,35),$$
$$4-(q+1,9,\lambda ),\text{where}\lambda \in \{63,147\}.$$