, then it cannot contain 0000, since otherwise it must omit one point from each of the four pairs formed from {0000, 0000} by permuting the indices, and must also omit one of {0000, 0000, 0000}, leading to at most 00 points in all; similarly, it cannot contain 0000, and so omits the entire diagonal {0000,0000,0000}, with two more points to be omitted. Similarly when 