MinT - Information on Result #1080859

Information on Result #1080859

Linear OOA(3⁸¹, 2097158, F₃, 4, 8) (dual of [(2097158, 4), 8388551, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵, 8, F₃, 4, 4) (dual of [(8, 4), 27, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁵, 8, F₃, 3, 4) (dual of [(8, 3), 19, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 5, 8)-net over F₃, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁷⁶, 2097150, F₃, 4, 8) (dual of [(2097150, 4), 8388524, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁰⁹, 4194316, F₃, 4, 8) (dual of [(4194316, 4), 16777155, 9]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3²⁴¹, 4194314, F₃, 4, 16) (dual of [(4194314, 4), 16777015, 17]-NRT-code)	[i]
3	Linear OOA(3²⁴², 4194316, F₃, 4, 16) (dual of [(4194316, 4), 16777022, 17]-NRT-code)	[i]
4	Linear OOA(3²⁴³, 4194319, F₃, 4, 16) (dual of [(4194319, 4), 16777033, 17]-NRT-code)	[i]
5	Linear OOA(3⁸¹, 2097157, F₃, 5, 8) (dual of [(2097157, 5), 10485704, 9]-NRT-code)	[i]	OOA Stacking with Additional Row
6	Linear OOA(3⁸¹, 2097157, F₃, 12, 8) (dual of [(2097157, 12), 25165803, 9]-NRT-code)	[i]	OOA Stacking with Additional Row