MinT - Information on Result #1222034

Information on Result #1222034

Digital (49, 60, 1678099)-net over F₂₇, using (u,Â u+v)-construction based on

digital (4, 9, 379)-net over F₂₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 2, 28)-net over F₂₇, using
    - kÂ =Â 2 construction [i]
  2. digital (2, 7, 351)-net over F₂₇, using
    - net defined by OOA [i] based on linear OOA(27⁷, 351, F₂₇, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(27⁷, 703, F₂₇, 5) (dual of [703, 696, 6]-code), using
        a code by Danev and Olsson [i]
digital (40, 51, 1677720)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁵¹, 1677720, F₂₇, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(27⁵¹, 8388601, F₂₇, 11) (dual of [8388601, 8388550, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁵¹, large, F₂₇, 11) (dual of [large, large−51, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (70, 81, 3356198)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets