MinT - Information on Result #1079333

Information on Result #1079333

Linear OOA(2⁹⁹, 2097158, F₂, 4, 9) (dual of [(2097158, 4), 8388533, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶, 8, F₂, 4, 4) (dual of [(8, 4), 26, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁶, 8, F₂, 3, 4) (dual of [(8, 3), 18, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (2, 6, 8)-net over F₂, using
    - hand-crafted matrix by Schmid and Wolf [i]
linear OOA(2⁹³, 2097150, F₂, 4, 9) (dual of [(2097150, 4), 8388507, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2⁹³, 8388600, F₂, 9) (dual of [8388600, 8388507, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁴¹, 4194309, F₂, 4, 9) (dual of [(4194309, 4), 16777095, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁴², 4194311, F₂, 4, 9) (dual of [(4194311, 4), 16777102, 10]-NRT-code)	[i]
3	Linear OOA(2¹⁴³, 4194316, F₂, 4, 9) (dual of [(4194316, 4), 16777121, 10]-NRT-code)	[i]
4	Linear OOA(2⁹⁹, 2097157, F₂, 5, 9) (dual of [(2097157, 5), 10485686, 10]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(2⁹⁹, 2097157, F₂, 6, 9) (dual of [(2097157, 6), 12582843, 10]-NRT-code)	[i]
6	Linear OOA(2⁹⁹, 2097157, F₂, 7, 9) (dual of [(2097157, 7), 14680000, 10]-NRT-code)	[i]
7	Linear OOA(2⁹⁹, 2097157, F₂, 8, 9) (dual of [(2097157, 8), 16777157, 10]-NRT-code)	[i]