MinT - Information on Result #2539955

Information on Result #2539955

Linear OOA(16⁴⁷, 643, F₁₆, 2, 20) (dual of [(643, 2), 1239, 21]-NRT-code), using 16¹ times duplication based on linear OOA(16⁴⁶, 643, F₁₆, 2, 20) (dual of [(643, 2), 1240, 21]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(16⁴⁴, 642, F₁₆, 2, 20) (dual of [(642, 2), 1240, 21]-NRT-code), using
- extracting embedded OOA [i] based on digital (24, 44, 642)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 22, 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 (27, 47, 643)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound