MinT - Information on Result #1026524

Information on Result #1026524

Linear OOA(3¹⁷⁸, 61, F₃, 3, 141) (dual of [(61, 3), 5, 142]-NRT-code), using juxtaposition based on

linear OOA(3³¹, 12, F₃, 3, 27) (dual of [(12, 3), 5, 28]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁴², 49, F₃, 3, 113) (dual of [(49, 3), 5, 114]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3³¹, 12, F₃, 3, 27) (dual of [(12, 3), 5, 28]-NRT-code) (see above)
  2. linear OOA(3¹⁰⁶, 37, F₃, 3, 85) (dual of [(37, 3), 5, 86]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3³¹, 12, F₃, 3, 27) (dual of [(12, 3), 5, 28]-NRT-code) (see above)
      2. linear OOA(3⁷⁰, 25, F₃, 3, 57) (dual of [(25, 3), 5, 58]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3³¹, 12, F₃, 3, 27) (dual of [(12, 3), 5, 28]-NRT-code) (see above)
        linear OOA(3³⁴, 13, F₃, 3, 29) (dual of [(13, 3), 5, 30]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 34, 13)-net over F₃, using
        net from sequence [i] based on digital (5, 12)-sequence over F₃, using
        Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 4, N(F)Â =Â 12, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁴, 73, F₃, 3, 169) (dual of [(73, 3), 5, 170]-NRT-code)	[i]		Juxtaposition for OOAs