Sec 275 says: No person to be a director of more than 15 companies.
Sec 278 says: In calculating, for the purposes of section 275, 276 and 277, the number of companies of which a person may be a director, the following companies shall be excluded, namely :-
(a) a private company which is neither a subsidiary nor a holding company of a public company;
(b) an unlimited company;
(c) an association not carrying on business for profit or which prohibits the payment of a dividend;
(d) a company in which such person is only an alternate director, that is to say, a director who is only qualified to act as such during the absence or incapacity of some other director.