MinT - Information on Result #2777226

Information on Result #2777226

Linear OOA(3²⁴⁴, 65, F₃, 4, 186) (dual of [(65, 4), 16, 187]-NRT-code), using strength reduction based on linear OOA(3²⁴⁴, 65, F₃, 4, 187) (dual of [(65, 4), 16, 188]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁹⁶, 28, F₃, 4, 81) (dual of [(28, 4), 16, 82]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,30P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹³², 37, F₃, 4, 105) (dual of [(37, 4), 16, 106]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 132, 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]

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(3²⁴⁸, 66, F₃, 4, 186) (dual of [(66, 4), 16, 187]-NRT-code)	[i]		NRT-Code Embedding in Larger Space