MinT - Information on Result #1079601

Information on Result #1079601

Linear OOA(2¹⁵⁰, 2097171, F₂, 4, 12) (dual of [(2097171, 4), 8388534, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹², 21, F₂, 4, 6) (dual of [(21, 4), 72, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 12, 21)-net over F₂, using
  - linear code embedding found in a computer search [i]
linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
  - discarding factors / shortening the dual code 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: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹⁴, 4194320, F₂, 4, 12) (dual of [(4194320, 4), 16777066, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹⁷, 4194342, F₂, 4, 12) (dual of [(4194342, 4), 16777151, 13]-NRT-code)	[i]
3	Linear OOA(2²¹⁴, 4194321, F₂, 4, 12) (dual of [(4194321, 4), 16777070, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁰, 2097171, F₂, 5, 12) (dual of [(2097171, 5), 10485705, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2¹⁵⁰, 2097171, F₂, 6, 12) (dual of [(2097171, 6), 12582876, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁵⁰, 2097171, F₂, 7, 12) (dual of [(2097171, 7), 14680047, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁵⁰, 2097171, F₂, 8, 12) (dual of [(2097171, 8), 16777218, 13]-NRT-code)	[i]
8	Digital (138, 150, 2097171)-net over F₂	[i]