MinT - Information on Result #1568311

Information on Result #1568311

Linear OOA(2¹⁷⁴, 2798249, F₂, 3, 12) (dual of [(2798249, 3), 8394573, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁶, 2048, F₂, 3, 6) (dual of [(2048, 3), 6108, 7]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³⁶, 2048, F₂, 2, 6) (dual of [(2048, 2), 4060, 7]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2³⁴, 2047, F₂, 2, 6) (dual of [(2047, 2), 4060, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F₂, using
      - 1 times m-reduction [i] based on digital (28, 35, 2047)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹³⁸, 2796201, F₂, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁷⁴, 2798249, F₂, 4, 12) (dual of [(2798249, 4), 11192822, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁴, 2798249, F₂, 5, 12) (dual of [(2798249, 5), 13991071, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁴, 2798249, F₂, 6, 12) (dual of [(2798249, 6), 16789320, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁴, 2798249, F₂, 7, 12) (dual of [(2798249, 7), 19587569, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁴, 2798249, F₂, 8, 12) (dual of [(2798249, 8), 22385818, 13]-NRT-code)	[i]
6	Digital (162, 174, 2798249)-net over F₂	[i]