MinT - Information on Result #896819

Information on Result #896819

Linear OOA(8¹¹⁰, 484, F₈, 2, 32) (dual of [(484, 2), 858, 33]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³², 130, F₈, 2, 16) (dual of [(130, 2), 228, 17]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 32, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 16, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
linear OOA(8⁷⁸, 354, F₈, 2, 32) (dual of [(354, 2), 630, 33]-NRT-code), using
- extracting embedded OOA [i] based on digital (46, 78, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 39, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

Mode: Constructive and 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(8¹¹¹, 484, F₈, 2, 32) (dual of [(484, 2), 857, 33]-NRT-code)	[i]		OOA Duplication