Nontotal boundedness of the Fréchet–Nikodym space of a nonatomic quasi-measure

Let A be a Boolean algebra and let μ be a nonatomic probability quasi-measure on A. Then there exists an infinite sequence (an) in A such that μ(ai△aj)>12 for all i≠j. The constant 12 is best possible. A similar problem concerning finite sequences in A is also considered and its connection with the theory of binary codes is established.