In contrast to Lagrange's Theorem in Finite Group Theory, we show that the ratio of the largest proper cwatset of degree d to the size of binary d-space approaches 1 as d approaches infinity. We show how to explicitly construct large cwatsets as cosets of Hamming Codes, and discuss many open questions that arise.
Davis, Matthew; Langley, Thomas M.; and Mazel, Norah, "Big Cwatsets and Hamming Code" (2005). Mathematical Sciences Technical Reports (MSTR). 52.