Data structure with search, insert and delete in amortised time $O(1)$?
NO.

Fredman and Saks proved that any data structure that supports these operations requires at least $\Omega(\log n/\log\log n)$ amortized time per operation.  (This is reference [1] in the paper by Dietz that you mention in your first comment.)  The lower bound holds in the very powerful cell probe model of computation, which only considers the number of distinct memory addresses accessed by the update and query algorithms.

Without some additional assumptions about the update and query operations, Dietz's data structure is the best possible (at least up to constant factors).