MinT - Information on Result #895049

Information on Result #895049

Linear OOA(3¹³⁴, 4194343, F₃, 2, 13) (dual of [(4194343, 2), 8388552, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹³, 42, F₃, 2, 6) (dual of [(42, 2), 71, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 13, 42)-net over F₃, using
  - linear code embedding found in a computer search [i]
linear OOA(3¹²¹, 4194301, F₃, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹²¹, 8388602, F₃, 13) (dual of [8388602, 8388481, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹³⁴, 4194343, F₃, 2, 12) (dual of [(4194343, 2), 8388552, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹³⁶, 4194344, F₃, 2, 13) (dual of [(4194344, 2), 8388552, 14]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3¹³⁵, 4194343, F₃, 2, 13) (dual of [(4194343, 2), 8388551, 14]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹³⁴, 4194343, F₃, 3, 13) (dual of [(4194343, 3), 12582895, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(3¹³⁴, 4194343, F₃, 4, 13) (dual of [(4194343, 4), 16777238, 14]-NRT-code)	[i]
6	Linear OOA(3¹³⁴, 4194343, F₃, 5, 13) (dual of [(4194343, 5), 20971581, 14]-NRT-code)	[i]
7	Digital (121, 134, 4194343)-net over F₃	[i]
8	Linear OOA(3¹³⁴, 2097171, F₃, 4, 13) (dual of [(2097171, 4), 8388550, 14]-NRT-code)	[i]	OOA Folding