MinT - Information on Result #1093634

Information on Result #1093634

Linear OOA(3²¹⁹, 77, F₃, 4, 105) (dual of [(77, 4), 89, 106]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷⁹, 37, F₃, 4, 52) (dual of [(37, 4), 69, 53]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 79, 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(3¹⁴⁰, 40, F₃, 4, 105) (dual of [(40, 4), 20, 106]-NRT-code), using
- constructionÂ X applied to AG(4;F,19P) âŠ‚ AG(4;F,24P) [i] based on
  1. linear OOA(3¹³¹, 36, F₃, 4, 105) (dual of [(36, 4), 13, 106]-NRT-code), using algebraic-geometric NRT-code AG(4;F,19P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  2. linear OOA(3¹²¹, 36, F₃, 4, 95) (dual of [(36, 4), 23, 96]-NRT-code), using algebraic-geometric NRT-code AG(4;F,24P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3⁹, 4, F₃, 4, 9) (dual of [(4, 4), 7, 10]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(4;7,3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁹, 77, F₃, 4, 104) (dual of [(77, 4), 89, 105]-NRT-code)	[i]		Strength Reduction for OOAs