MinT - Information on Result #1209897

Information on Result #1209897

Digital (30, 36, 21853)-net over F₄, using (u,Â u+v)-construction based on

digital (0, 3, 5)-net over F₄, using
- net from sequence [i] based on digital (0, 4)-sequence over F₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 0 and N(F) ≥ 5, using
    - the rational function field F₄(x) [i]
  - Niederreiter sequence [i]
digital (27, 33, 21848)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4³³, 21848, F₄, 6, 6) (dual of [(21848, 6), 131055, 7]-NRT-code), using
  - OA 3-folding and stacking [i] based on linear OA(4³³, 65544, F₄, 6) (dual of [65544, 65511, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(4³³, 65536, F₄, 6) (dual of [65536, 65503, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(4²⁵, 65536, F₄, 5) (dual of [65536, 65511, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(4⁰, 8, F₄, 0) (dual of [8, 8, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (160, 172, 5614253)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
2	Digital (132, 145, 1419953)-net over F₄	[i]
3	Digital (171, 184, 5614253)-net over F₄	[i]