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

Let U β be the special Buekenhout-Metz unital in PG ( 2 , q 2 ) , formed by a union of q conics, where q = p e is an odd prime power. It can be shown that the dimension of the binary code of the corresponding unital design U β is less than or equal to q 3 + 1 − q . Baker and Wantz conjectured that equality holds. We prove that the aforementioned dimension is greater than or equal to q 3 ( 1 − 1 p ) + q 2 p .