On the dimensions of the binary codes of a class of unitals

Let UβUβ be the special Buekenhout-Metz unital in PG(2,q2)PG(2,q2), formed by a union of qq conics, where q=peq=pe is an odd prime power. It can be shown that the dimension of the binary code of the corresponding unital design UβUβ is less than or equal to q3+1−qq3+1−q. Baker and Wantz conjectured that equality holds. We prove that the aforementioned dimension is greater than or equal to q3(1−1p)+q2p.