MinT - Information on Result #1093621

Information on Result #1093621

Linear OOA(3²¹¹, 78, F₃, 4, 99) (dual of [(78, 4), 101, 100]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷⁶, 37, F₃, 4, 49) (dual of [(37, 4), 72, 50]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 76, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
linear OOA(3¹³⁵, 41, F₃, 4, 99) (dual of [(41, 4), 29, 100]-NRT-code), using
- constructionÂ X applied to AG(4;F,22P) âŠ‚ AG(4;F,27P) [i] based on
  1. linear OOA(3¹²⁵, 36, F₃, 4, 99) (dual of [(36, 4), 19, 100]-NRT-code), using algebraic-geometric NRT-code AG(4;F,22P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  2. linear OOA(3¹¹⁵, 36, F₃, 4, 89) (dual of [(36, 4), 29, 90]-NRT-code), using algebraic-geometric NRT-code AG(4;F,27P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3¹⁰, 5, F₃, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3¹⁰, 7, F₃, 4, 9) (dual of [(7, 4), 18, 10]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,18P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [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(3²¹², 78, F₃, 4, 99) (dual of [(78, 4), 100, 100]-NRT-code)	[i]		OOA Duplication