A bound for plany Kakeya sets in ${\mathbb{F}}_q^4$ using the planebrush method

Izabella Łaba, Mukul Rai Choudhuri, Joshua Zahl

Katz and Zahl used a planebrush argument to prove that Kakeya sets in ${\mathbb{R}}^4$ have Hausdorff dimension at least 3.059. In the special case when the Kakeya set is plany, thei…