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On the other hand, there are examples<ref>{{cite doi|10.1016/0001-8708(82)90048-2}}</ref> where the Gröbner basis contains elements of degree
:<math>d^{2^{\Omega(n)}}</math>,
and above upper bound of complexity is almost optimal, up to a constant factor in the second exponent). Nevertheless, such examples are extremely
Since its discovery, many variants of Buchberger's have been introduced to improve its efficiency. [[Faugère's F4 and F5 algorithms]] are presently the most efficient algorithms for computing Gröbner bases, and allow to compute routinely Gröbner bases consisting of several hundreds of polynomials, having each several hundreds of terms and coefficients of several hundreds of digits.
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