MinT - Information on Result #1466392

Information on Result #1466392

Linear OOA(3²¹⁰, 4194432, F₃, 2, 19) (dual of [(4194432, 2), 8388654, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁹, 131, F₃, 2, 9) (dual of [(131, 2), 233, 10]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁹, 131, F₃, 9) (dual of [131, 102, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁹, 140, F₃, 9) (dual of [140, 111, 10]-code), using
    - a â€œBZâ€ code from Brouwerâ€™s database [i]
linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²¹⁰, 4194432, F₃, 3, 19) (dual of [(4194432, 3), 12583086, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²¹⁰, 4194432, F₃, 4, 19) (dual of [(4194432, 4), 16777518, 20]-NRT-code)	[i]
3	Linear OOA(3²¹⁰, 4194432, F₃, 5, 19) (dual of [(4194432, 5), 20971950, 20]-NRT-code)	[i]
4	Digital (191, 210, 4194432)-net over F₃	[i]