If no tickets are found when you do a search, it means that at moment we do not have any available. For big releases, tickets are reserved very quickly. They are reserved for a limited time to allow customers with tickets in their 'baskets' to either complete the purchase or release the tickets.
If the purchase is completed, the ticket becomes unavailable and when this occurs for all tickets in a section, this section and price category will disappear or be crossed out from the purchase flow. If the purchase is not completed, the ticket will be released back into the system and be allocated to the next customer with a matching search.
When a lot of tickets are held in purchases that have not yet been completed, the tickets will not show up in a search because at the moment they are not available. However, the website will not state that they are sold out unless each and every ticket has been paid for.
Unfortunately, for some events the demand will exceed the supply.