MinT - Information on Result #1227612

Information on Result #1227612

Digital (37, 48, 1680960)-net over F₈₁, using (u,Â u+v)-construction based on

digital (2, 7, 3240)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁷, 3240, F₈₁, 5, 5) (dual of [(3240, 5), 16193, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(81⁷, 3240, F₈₁, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
      - a code by Danev and Olsson [i]
digital (30, 41, 1677720)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁴¹, 1677720, F₈₁, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(81⁴¹, 8388601, F₈₁, 11) (dual of [8388601, 8388560, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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 (38, 49, 1680960)-net over F₈₁	[i]		Net Duplication