There is some context why/how ring dimesion changed by increasing mult_depth value. If i increment mult_depth from 1 to 4 my ring dimesion is 16384. And after 4 to 7 is 32768. After 7 i get approximation error
The mult_depth (along with firstModSize, scalingModSize etc) determines the ciphertext modulus. If you set a security level (by default it is HEStd_128_classic), then a ring dimension is chosen to achieve this security level given the ciphertext modulus, according to the tables in http://homomorphicencryption.org/wp-content/uploads/2018/11/HomomorphicEncryptionStandardv1.1.pdf.
Please watch the introductory webinars here in order to learn more about these concepts.
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