MinT - Information on Result #1210610

Information on Result #1210610

Digital (144, 161, 1048609)-net over F₄, using (u,Â u+v)-construction based on

digital (8, 16, 34)-net over F₄, using
- trace code for nets [i] based on digital (0, 8, 17)-net over F₁₆, using
  - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
      - the rational function field F₁₆(x) [i]
    - Niederreiter sequence [i]
digital (128, 145, 1048575)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁴⁵, 1048575, F₄, 17, 17) (dual of [(1048575, 17), 17825630, 18]-NRT-code), using
  - OOA 8-folding and stacking with additional row [i] based on linear OA(4¹⁴⁵, 8388601, F₄, 17) (dual of [8388601, 8388456, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, large, F₄, 17) (dual of [large, large−145, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (145, 161, 1048609)-net over F₄	[i]		t-Expansion
2	Digital (145, 162, 1048609)-net over F₄	[i]		Net Duplication