MinT - Information on Result #895229

Information on Result #895229

Linear OOA(3¹⁹⁹, 4194327, F₃, 2, 18) (dual of [(4194327, 2), 8388455, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 26, F₃, 2, 9) (dual of [(26, 2), 33, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 14, F₃, 2, 4) (dual of [(14, 2), 22, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 6, 14)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹³, 13, F₃, 2, 9) (dual of [(13, 2), 13, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 13, 13)-net over F₃, using
      - a shift-net [i]
linear OOA(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁹⁹, 4194327, F₃, 3, 18) (dual of [(4194327, 3), 12582782, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁹⁹, 4194327, F₃, 4, 18) (dual of [(4194327, 4), 16777109, 19]-NRT-code)	[i]
3	Linear OOA(3¹⁹⁹, 4194327, F₃, 5, 18) (dual of [(4194327, 5), 20971436, 19]-NRT-code)	[i]
4	Digital (181, 199, 4194327)-net over F₃	[i]
5	Linear OOA(3¹⁹⁹, 2097163, F₃, 4, 18) (dual of [(2097163, 4), 8388453, 19]-NRT-code)	[i]	OOA Folding