The Collaborative International Dictionary of English v.0.48:

Nonadmission \Non`ad*mis"sion\, n.
   Failure to be admitted.
   [1913 Webster] nonadsorbent

Moby Thesaurus II by Grady Ward, 1.0:

24 Moby Thesaurus words for "nonadmission":
   ban, bar, barring, blockade, boycott, circumscription, debarment,
   debarring, demarcation, embargo, exception, exclusion,
   inadmissibility, injunction, lockout, narrowing, omission,
   preclusion, prohibition, rejection, relegation, repudiation,
   restriction, taboo