MinT - Information on Result #895351

Information on Result #895351

Linear OOA(3²⁴¹, 4194361, F₃, 2, 22) (dual of [(4194361, 2), 8388481, 23]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁰, 60, F₃, 2, 11) (dual of [(60, 2), 90, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (19, 30, 60)-net over F₃, using
  - trace code for nets [i] based on digital (4, 15, 30)-net over F₉, using
    - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
        a function field by SÃ©mirat [i]
linear OOA(3²¹¹, 4194301, F₃, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹¹, 8388602, F₃, 22) (dual of [8388602, 8388391, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹¹, large, F₃, 22) (dual of [large, large−211, 23]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁴², 4194361, F₃, 2, 22) (dual of [(4194361, 2), 8388480, 23]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²⁴¹, 3979850, F₃, 3, 22) (dual of [(3979850, 3), 11939309, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3²⁴¹, 3979850, F₃, 4, 22) (dual of [(3979850, 4), 15919159, 23]-NRT-code)	[i]
4	Linear OOA(3²⁴¹, 3979850, F₃, 5, 22) (dual of [(3979850, 5), 19899009, 23]-NRT-code)	[i]
5	Digital (219, 241, 3979850)-net over F₃	[i]
6	Linear OOA(3²⁴¹, 2097180, F₃, 4, 22) (dual of [(2097180, 4), 8388479, 23]-NRT-code)	[i]	OOA Folding