MinT - Information on Result #1026468

Information on Result #1026468

Linear OOA(3²⁴⁹, 85, F₃, 3, 192) (dual of [(85, 3), 6, 193]-NRT-code), using juxtaposition based on

linear OOA(3⁴², 16, F₃, 3, 35) (dual of [(16, 3), 6, 36]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3²⁰¹, 69, F₃, 3, 156) (dual of [(69, 3), 6, 157]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3³³, 13, F₃, 3, 28) (dual of [(13, 3), 6, 29]-NRT-code), using
    - extracting embedded OOA [i] based on digital (5, 33, 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]
  2. linear OOA(3¹⁶², 56, F₃, 3, 127) (dual of [(56, 3), 6, 128]-NRT-code), using
    - repeating each code word 2 times [i] based on linear OOA(3⁷⁸, 28, F₃, 3, 63) (dual of [(28, 3), 6, 64]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,20P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, 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(3²⁴⁹, 85, F₃, 3, 191) (dual of [(85, 3), 6, 192]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁴⁹, 85, F₃, 3, 190) (dual of [(85, 3), 6, 191]-NRT-code)	[i]		Strength Reduction for OOAs