Someone may provide an alternative word but, as a native french speaker, I absolutely find "nombre de participants" right, here.

« Nombre des qualifiés » est une amélioration de « nombre des participants ». Je ne vois pas d’autre terme, en particulier aucun terme d’un seul mot.

French native here. The correct word, particularly in this case (a large field of competitors), would be the word plateau.

Sport journals will often talk about "un plateau relevé" to indicate that the field is very competitive for a given tournament, particularly tennis.