MinT - Information on Result #2539943

Information on Result #2539943

Linear OOA(16⁴⁴, 643, F₁₆, 2, 19) (dual of [(643, 2), 1242, 20]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(16⁴², 642, F₁₆, 2, 19) (dual of [(642, 2), 1242, 20]-NRT-code), using

extracting embedded OOA [i] based on digital (23, 42, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 21, 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	Linear OOA(16⁴⁵, 643, F₁₆, 2, 19) (dual of [(643, 2), 1241, 20]-NRT-code)	[i]		OOA Duplication
2	Digital (25, 44, 643)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound