We show that a Magma implementation of Joux's L[1/4+o(1)] algorithm
can be used to compute discrete logarithms in the 1303-bit finite field
F_{3^{6*137}} and the 1551-bit finite field F_{3^{6*163}} with very modest computational resources. Our F_{3^{6*137}} implementation was the first to illustrate the effectiveness of
Joux's algorithm for computing discrete logarithms in small-characteristic
finite fields that are not Kummer or twisted-Kummer extensions.
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