The author of the Wikipedia article is conflating salt with the idea of search space, implying salt is a way to deter brute force attacks. Security is not improved by confusing these ideas; someone who can't recognize and delineate these two issues is not a credible guide.
The purpose of salt is to thwart pre-computed lookup tables (like a Rainbow table). Salt prevents an attacker from trading "space" for "time." Every bit of salt doubles the storage requirements for a table; a two byte salt makes a big (65536 times) difference, but eight bytes would require non-existent "yottabyte" storage devices for lookup tables.
Assuming that the salt cannot be kept secret encourages better key-strengthening and password selection, and this leads to more secure system.
However, recent recommendations from NIST encourage the use of an additional, secret "salt" (I've seen others call this additional secret "pepper"). One additional iteration of the key derivation can be performed using this secret as a salt. Rather than increasing strength against a pre-computed lookup attack, this round protects against live dictionary attacks. In this way, it's more like the large number of iterations in a good key derivation function.
This secret serves no purpose if stored with the hashed password; it must be managed as a secret, and that could be difficult in a large user database.
Brute force attacks are best prevented by key-strengthening (applying the hash function thousands of times), and password selection rules (require longer passwords, reject blacklisted entries, etc.), but a "pepper" provides an additional layer of defense.
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