Abstract: | Hyperovals in projective planes turn out to have a link with t‐designs. Motivated by an unpublished work of Lonz and Vanstone, we present a construction for t‐designs and s‐resolvable t‐designs from hyperovals in projective planes of order . We prove that the construction works for . In particular, for the construction yields a family of 5‐ designs. For numerous infinite families of 4‐designs on points with block size can be constructed for any . The construction assumes the existence of a 4‐ design, called the indexing design, including the complete 4‐ design. Moreover, we prove that if the indexing design is s‐resolvable, then so is the constructed design. As a result, many of the constructed designs are s‐resolvable for . We include a short discussion on the simplicity or non‐simplicity of the designs from hyperovals. |