MinT - Information on Result #1079734

Information on Result #1079734

Linear OOA(2¹⁶⁰, 2097277, F₂, 4, 13) (dual of [(2097277, 4), 8388948, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 127, F₂, 4, 6) (dual of [(127, 4), 487, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
  - linear code embedding found in a computer search [i]
linear OOA(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’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(2¹⁶⁰, 2097277, F₂, 4, 12) (dual of [(2097277, 4), 8388948, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁶¹, 2097277, F₂, 4, 13) (dual of [(2097277, 4), 8388947, 14]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²²⁷, 4194554, F₂, 4, 13) (dual of [(4194554, 4), 16777989, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
4	Linear OOA(2¹⁶⁰, 2097277, F₂, 5, 13) (dual of [(2097277, 5), 10486225, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2¹⁶⁰, 2097277, F₂, 6, 13) (dual of [(2097277, 6), 12583502, 14]-NRT-code)	[i]
6	Linear OOA(2¹⁶⁰, 2097277, F₂, 7, 13) (dual of [(2097277, 7), 14680779, 14]-NRT-code)	[i]
7	Linear OOA(2¹⁶⁰, 2097277, F₂, 8, 13) (dual of [(2097277, 8), 16778056, 14]-NRT-code)	[i]
8	Digital (147, 160, 2097277)-net over F₂	[i]