Number of keystreams generated in Kreyvium for a single key/IV pair Kreyvium employs 128-bit key and 128-bit IV. By a single initialization procedure using a key/IV pair, how many keystreams can be generated?
Trivium is designed as an 80-bit key and 80-bit $\operatorname{IV}$. Noted in Algorithms, key size and parameters report 2014. Technical report, ENISA - European Union Agency
for Network and Information Security, 2014. increasing the key size was not an easy task.

Kreyvium is defined in Stream ciphers: A Practical Solution for Efficient
Homomorphic-Ciphertext Compression by Canteaut et al. as 128-bit IV and 128-bit key variant of Trivium. Actually they consider a solution to this problem.


  In typical applications of homomorphic encryption, the first step consists for Alice to encrypt some plaintext m under Bob’s public key pk and to send the ciphertext $c = \operatorname{HE}_{pk}(m)$ to some third-party evaluator Charlie. This paper specifically considers that first step, i.e. the problem of transmitting $c$ as efficiently as possible from Alice to Charlie. 


They gave the maximum length as


  Our first aim is to offer a variant of Trivium with 128-bit key and $\operatorname{IV}$, without increasing the multiplicative depth of the corresponding circuit. Besides a higher security level, another advantage of this variant is that the number of possible $\operatorname{IVs}$, and then the maximal length of data which can be encrypted under the same key, increases from $2^{80}N_{trivium}(d)$ to $2^{128}N_{kreyvium}(d)$. 


Bolds are mine



What is the Kreyvium

A picture can tell a thousand words. From the article;



They added the 256-bit IV and key bits into 288-bit internal state. Full defitinion can be found on the 8th page of the article.