Proposed by Marc van Dongen

This problem has its roots in Bioinformatics and Coding Theory.

Problem: find as large a set *S* of strings (words) of length *8* over the alphabet *W = { A,C,G,T }* with the following properties:

- Each word in
*S*has*4*symbols from*{ C,G }*; - Each pair of distinct words in
*S*differ in at least*4*positions; and - Each pair of words
*x*and*y*in*S*(where*x*and*y*may be identical) are such thatx and^{R}y differ in at least^{C}4 positions. Here,( x is the reverse of_{1},…,x_{8})^{R}= ( x_{8},…,x_{1})( x and_{1},…,x_{8})( y is the Watson-Crick complement of_{1},…,y_{8})^{C}( y , i.e. the word where each_{1},…,y_{8})A is replaced by aT and vice versa and eachC is replaced by aG and vice versa.