MinT - Information on Result #2777241

Information on Result #2777241

Linear OOA(3²⁴⁴, 69, F₃, 4, 162) (dual of [(69, 4), 32, 163]-NRT-code), using strength reduction based on linear OOA(3²⁴⁴, 69, F₃, 4, 165) (dual of [(69, 4), 32, 166]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁹⁶, 32, F₃, 4, 75) (dual of [(32, 4), 32, 76]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,52P) [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹¹⁶, 37, F₃, 4, 89) (dual of [(37, 4), 32, 90]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 116, 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		Method
1	Linear OOA(3²³⁰, 65, F₃, 4, 148) (dual of [(65, 4), 30, 149]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(3²²⁹, 65, F₃, 4, 147) (dual of [(65, 4), 31, 148]-NRT-code)	[i]
3	Linear OOA(3²²⁸, 65, F₃, 4, 146) (dual of [(65, 4), 32, 147]-NRT-code)	[i]