MinT - Information on Result #2805917

Information on Result #2805917

Linear OOA(3²³⁰, 86, F₃, 4, 103) (dual of [(86, 4), 114, 104]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²²⁶, 85, F₃, 4, 103) (dual of [(85, 4), 114, 104]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁷⁸, 37, F₃, 4, 51) (dual of [(37, 4), 70, 52]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 78, 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]
2. linear OOA(3¹⁴⁸, 48, F₃, 4, 103) (dual of [(48, 4), 44, 104]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,88P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, 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(3²³¹, 86, F₃, 4, 103) (dual of [(86, 4), 113, 104]-NRT-code)	[i]		OOA Duplication