MinT - Information on Result #1026107

Information on Result #1026107

Linear OOA(3¹⁸⁸, 67, F₃, 3, 129) (dual of [(67, 3), 13, 130]-NRT-code), using juxtaposition based on

linear OOA(3²⁶, 13, F₃, 3, 21) (dual of [(13, 3), 13, 22]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 26, 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]
linear OOA(3¹⁴⁹, 54, F₃, 3, 107) (dual of [(54, 3), 13, 108]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(3⁶⁸, 27, F₃, 3, 53) (dual of [(27, 3), 13, 54]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,27P) [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(3¹⁸⁸, 67, F₃, 3, 128) (dual of [(67, 3), 13, 129]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁸⁸, 67, F₃, 3, 127) (dual of [(67, 3), 13, 128]-NRT-code)	[i]		Strength Reduction for OOAs