Quantum jump codes are quantum error-correcting codes which correct errors caused by quantum jumps. A t-spontaneous emission error design ( t-SEED) was introduced by Beth et al. in 2003 [T. Beth, C. Charnes, M. Grassl, G. Alber, A. Delgado, and M. Mussinger, A new class of designs which protect against quantum jumps, Des Codes Cryptogr 29 (2003), 51-70.] to construct quantum jump codes. The number of designs (dimension) in a t-SEED corresponds to the number of orthogonal basis states in a quantum jump code. A nondegenerate t-SEED is optimal if it has the largest possible dimension. In this paper, we investigate the bounds on the dimensions of 2-SEEDs systematically. The exact dimensions of optimal 2- [ABSTRACT FROM AUTHOR]