Can I use my competitor's brands to improve my website ranking?
You can the improve your website's ranking on Google by:
Search Engine Marketing ("SEM"). This involves purchasing keywords from Google (known as "Google AdWords") which can cause an advertisement for your website to appear above Google's organic search results when a user uses searches for keywords; and/or
Search Engine Optimisation ("SEO"). This involves using terms as 'metatags' in the source code of your website to make the your website appear in Google's organic search results.
In Veda Advantage Ltd v Malouf Group Enterprises Pty Ltd  FCA 255, the Federal Court held that the use of a registered trade mark as a Google AdWord (SEM) was not "use" of a trade mark and therefore does not amount to trade mark infringement.
In Accor Australia & New Zealand Hospitality Pty Ltd v Liv Pty Ltd  FCAFC 56, the Full Federal Court held that use of another's registered trade mark in your website's source code (SEO) was use of of a trade mark and therefore does amount to trade mark infringement.
This is because Google AdWords are not visible to customers and therefore cannot function as a trade mark. However, anyone can access the source code of a website by right clicking on it and selecting "view source." Liv Pty Ltd could not argue that it was merely using it's competitor's trade mark in a descriptive sense, which would otherwise act as a defence to infringement.