MinT - Information on Result #1129628

Information on Result #1129628

Linear OOA(3²¹⁸, 75, F₃, 5, 107) (dual of [(75, 5), 157, 108]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁸⁰, 37, F₃, 5, 53) (dual of [(37, 5), 105, 54]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 80, 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]
linear OOA(3¹³⁸, 38, F₃, 5, 107) (dual of [(38, 5), 52, 108]-NRT-code), using
- constructionÂ X applied to AG(5;F,36P) âŠ‚ AG(5;F,39P) [i] based on
  1. linear OOA(3¹³³, 36, F₃, 5, 107) (dual of [(36, 5), 47, 108]-NRT-code), using algebraic-geometric NRT-code AG(5;F,36P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  2. linear OOA(3¹²⁷, 36, F₃, 5, 101) (dual of [(36, 5), 53, 102]-NRT-code), using algebraic-geometric NRT-code AG(5;F,39P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3⁵, 2, F₃, 5, 5) (dual of [(2, 5), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁵, 3, F₃, 5, 5) (dual of [(3, 5), 10, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(5;10,3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁸, 75, F₃, 5, 106) (dual of [(75, 5), 157, 107]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²¹⁹, 75, F₃, 5, 107) (dual of [(75, 5), 156, 108]-NRT-code)	[i]		OOA Duplication