Some questions about possibly nonsensical ideas:
1) Can you come up with a definition of an infinite association scheme ?
2) Would infinite association schemes relate to infinite groups the way association schemes relate to finite groups ? (see http://www.ams.org/bull/2006-43-02/S0273-0979-05-01077-3/S0273-0979-05-01077-3.pdf)
3) Can you define objects that relate to semigroups and quasigroups as schemes relate to groups ?
4) What combinatorial, statistical or other properties would these infinite schemes, semi-schemes and quasi-schemes have ?