MinT - Information on Result #2540268

Information on Result #2540268

Linear OOA(16¹¹⁷, 644, F₁₆, 2, 54) (dual of [(644, 2), 1171, 55]-NRT-code), using 16¹ times duplication based on linear OOA(16¹¹⁶, 644, F₁₆, 2, 54) (dual of [(644, 2), 1172, 55]-NRT-code), using

2 times NRT-code embedding in larger space [i] based on linear OOA(16¹¹², 642, F₁₆, 2, 54) (dual of [(642, 2), 1172, 55]-NRT-code), using
- extracting embedded OOA [i] based on digital (58, 112, 642)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 56, 321)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
        sharp bound on the number of rational points on curves with genus 2 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (63, 117, 644)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound